> printlevel:=100: > int((sin(x)/x)^5,x); {--> enter sin, args = x sin(x) := sin(x) <-- exit sin (now at top level) = sin(x)} #01 {--> enter int, args = sin(x)^5/x^5, x #02 {--> enter int/int, args = [sin(x)^5/x^5, x], 10, _EnvCauchyPrincipalValue #03 {--> enter int/check_syntax, args = [sin(x)^5/x^5, x] answer := FAIL n := 2 5 sin(x) ff := ------- 5 x llimits := x 5 sin(x) answer := [-------, x] 5 x opts := [] opts := [] opts := [formula] opt := formula 5 sin(x) answer := [-------, x, [formula]] 5 x 5 sin(x) [-------, x, [formula]] 5 x <-- exit int/check_syntax (now in int/int) = [sin(x)^5/x^5, x, [formula]]} 5 sin(x) answer := [-------, x, [formula]] 5 x #04 {--> enter int/tools/rename, args = [sin(x)^5/x^5, x, [formula]] known_bound_fns := {int, sum, product, limit, Int, Limit, Sum, Product} affected_vars := [] forw_subs := [] {--> enter unknown, args = x false <-- exit unknown (now in int/tools/rename) = false} {--> enter unknown, args = formula false <-- exit unknown (now in int/tools/rename) = false} symb := {} forw_subs := [] back_subs := [] value remembered (in int/tools/rename): sin(x) -> sin(x) 5 sin(x) [[-------, x, [formula]], []] 5 x <-- exit int/tools/rename (now in int/int) = [[sin(x)^5/x^5, x, [formula]], []]} 5 sin(x) answer := [[-------, x, [formula]], []] 5 x lt := [] 5 sin(x) answer := [-------, x, [formula]] 5 x #05 {--> enter int/indefinite, args = sin(x)^5/x^5, x, [formula] opts := formula {--> enter int/indef0, args = sin(x)^5/x^5, x 5 sin(_X) f := -------- 5 _X #06 {--> enter int/indef1, args = sin(_X)^5/_X^5 table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) 5 sin(_X) answer := int/itable[--------] 5 _X #07 answer := int/indef1/NOVAL #08 {--> enter remove, args = has, sin(_X)^5/_X^5, _X {--> enter unknown, args = sin(_X)^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} 1 <-- exit remove (now in int/indef1) = 1} #09 c := 1 5 sin(_X) g := -------- 5 _X #10 {--> enter type/radfun, args = sin(_X)^5/_X^5, anything, _X v := {_X} r := sin(_X) <-- exit type/radfun (now in int/indef1) = false} #11 {--> enter int/indef2, args = sin(_X)^5/_X^5 {--> enter unknown, args = _X _X <-- exit unknown (now in int/indef2) = _X} {--> enter unknown, args = sin(_X) sin(_X) <-- exit unknown (now in int/indef2) = sin(_X)} inds := {_X, sin(_X)} {--> enter unknown, args = _X <-- exit unknown (now in int/indef2) = } {--> enter unknown, args = sin(_X) sin(_X) <-- exit unknown (now in int/indef2) = sin(_X)} fcns := {sin(_X)} algs := {} bases := {} {--> enter unknown, args = sin(_X) _X <-- exit unknown (now in int/indef2) = _X} fargs := {_X} {--> enter unknown, args = sin(_X) sin <-- exit unknown (now in int/indef2) = sin} fnames := {sin} {--> enter int/denoms, args = sin(_X)^5/_X^5 {--> enter sin, args = _X sin(_X) := sin(_X) #12 <-- exit sin (now in int/denoms) = sin(_X)} {--> enter int/denoms, args = sin(_X)^5 value remembered (in int/denoms): sin(_X) -> sin(_X) {--> enter int/denoms, args = sin(_X) value remembered (in int/denoms): sin(_X) -> sin(_X) {--> enter int/denoms, args = _X {} <-- exit int/denoms (now in int/denoms) = {}} {} <-- exit int/denoms (now in int/denoms) = {}} value remembered (in int/denoms): sin(_X) -> sin(_X) {--> enter int/denoms, args = 5 {} <-- exit int/denoms (now in int/denoms) = {}} {} <-- exit int/denoms (now in int/denoms) = {}} value remembered (in int/denoms): sin(_X) -> sin(_X) {--> enter int/denoms, args = 1/_X^5 value remembered (in int/denoms): int/denoms(_X) -> {} {_X} <-- exit int/denoms (now in int/denoms) = {_X}} {_X} <-- exit int/denoms (now in int/indef2) = {_X}} denoms := {_X} dummies := {} #13 {--> enter remove, args = depends, {_X, sin(_X)}, {} {--> enter unknown, args = _X, {} {--> enter depends, args = _X, {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {--> enter unknown, args = sin(_X), {} {--> enter depends, args = sin(_X), {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {_X, sin(_X)} <-- exit remove (now in int/indef2) = {_X, sin(_X)}} ddset := {_X, sin(_X)} z := _X dz := 1 z := sin(_X) {--> enter diff/sin, args = _X, _X {--> enter cos, args = _X cos(_X) := cos(_X) <-- exit cos (now in diff/sin) = cos(_X)} cos(_X) <-- exit diff/sin (now in int/indef2) = cos(_X)} dz := cos(_X) 5 _Y t := ----------- 5 _X cos(_X) #14 {--> enter int/trigon, args = sin(_X)^5/_X^5 {--> enter type/radext, args = sin(_X)^5/_X^5 false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = sin(_X)^5 false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = sin(_X) false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = _X false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = 5 false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = 1/_X^5 false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = -5 false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = sin(_X)^5/_X^5, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = sin(_X)^5, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = sin(_X), constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = _X, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = 5, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = 1/_X^5, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter type/radext, args = -5, constant false <-- exit type/radext (now in int/trigon) = false} {--> enter unknown, args = sin(_X) sin(_X) <-- exit unknown (now in int/trigon) = sin(_X)} {--> enter unknown, args = sin(_X) <-- exit unknown (now in int/trigon) = } ff := {} 5 sin(_X) ff := -------- 5 _X 5 Y ffx := --- 5 _X dx := -5 ds := 5 dc := 0 #15 {--> enter int/xsincos, args = -5, 5, 0 {--> enter trig/tfourier, args = 5, 0, _X {--> enter tfourier/sin, args = 5 x := _X x := _X #16 {--> enter sum, args = (-1)^k*binomial(5,k)*sin((5-2*k)*x), k = 0 .. 2 xx := k has_diffs := false {--> enter type/RootOf, args = 0 .. 2 false <-- exit type/RootOf (now in sum) = false} xx := k a := 0 b := 3 dab := 3 dxx := FAIL {--> enter binomial, args = 5, 0 1 <-- exit binomial (now in sum) = 1} {--> enter sin, args = 5*_X {--> enter csgn, args = 5 z := 5 <-- exit csgn (now in sin) = 1} sin(5 _X) := sin(5 _X) <-- exit sin (now in sum) = sin(5*_X)} {--> enter binomial, args = 5, 1 c := 1 c := 5 binomial/a := 5 binomial/b := 1 binomial/c := 5 <-- exit binomial (now in sum) = 5} {--> enter sin, args = 3*_X {--> enter csgn, args = 3 z := 3 <-- exit csgn (now in sin) = 1} sin(3 _X) := sin(3 _X) <-- exit sin (now in sum) = sin(3*_X)} {--> enter binomial, args = 5, 2 c := 5 c := 10 binomial/b := 2 binomial/c := 10 <-- exit binomial (now in sum) = 10} value remembered (in sum): sin(_X) -> sin(_X) sin(5 _X) - 5 sin(3 _X) + 10 sin(_X) <-- exit sum (now in tfourier/sin) = sin(5*_X)-5*sin(3*_X)+10*sin(_X)} 2 sin(5 _X) - 10 sin(3 _X) + 20 sin(_X) <-- exit tfourier/sin (now in trig/tfourier) = 2*sin(5*_X)-10*sin(3*_X)+20*sin(_X)} 1/16 sin(5 _X) - 5/16 sin(3 _X) + 5/8 sin(_X) <-- exit trig/tfourier (now in int/xsincos) = 1/16*sin(5*_X)-5/16*sin(3*_X)+5/8*sin(_X)} #17 {--> enter int/indef1, args = 1/16/_X^5*sin(5*_X)-5/16/_X^5*sin(3*_X)+5/8/_X^5*sin(_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(5 _X) sin(3 _X) sin(_X) answer := int/itable[1/16 --------- - 5/16 --------- + 5/8 -------] 5 5 5 _X _X _X answer := int/indef1/NOVAL #18 {--> enter int/indef1, args = 1/16/_X^5*sin(5*_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(5 _X) answer := int/itable[1/16 ---------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 1/16/_X^5*sin(5*_X), _X {--> enter unknown, args = 1/16, _X true <-- exit unknown (now in remove) = true} {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = sin(5*_X), _X false <-- exit unknown (now in remove) = false} 1/16 <-- exit remove (now in int/indef1) = 1/16} c := 1/16 sin(5 _X) g := --------- 5 _X #19 {--> enter int/indef1, args = 1/_X^5*sin(5*_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(5 _X) answer := int/itable[---------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 1/_X^5*sin(5*_X), _X {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = sin(5*_X), _X false <-- exit unknown (now in remove) = false} 1 <-- exit remove (now in int/indef1) = 1} c := 1 sin(5 _X) g := --------- 5 _X {--> enter type/radfun, args = 1/_X^5*sin(5*_X), anything, _X v := {_X} r := sin(5 _X) <-- exit type/radfun (now in int/indef1) = false} #20 {--> enter int/indef2, args = 1/_X^5*sin(5*_X) {--> enter unknown, args = sin(5*_X) sin(5 _X) <-- exit unknown (now in int/indef2) = sin(5*_X)} {--> enter unknown, args = _X _X <-- exit unknown (now in int/indef2) = _X} inds := {sin(5 _X), _X} {--> enter unknown, args = sin(5*_X) sin(5 _X) <-- exit unknown (now in int/indef2) = sin(5*_X)} {--> enter unknown, args = _X <-- exit unknown (now in int/indef2) = } fcns := {sin(5 _X)} algs := {} bases := {} {--> enter unknown, args = sin(5*_X) 5 _X <-- exit unknown (now in int/indef2) = 5*_X} fargs := {5 _X} {--> enter unknown, args = sin(5*_X) sin <-- exit unknown (now in int/indef2) = sin} fnames := {sin} {--> enter int/denoms, args = 1/_X^5*sin(5*_X) value remembered (in int/denoms): sin(5*_X) -> sin(5*_X) value remembered (in int/denoms): int/denoms(1/_X^5) -> {_X} value remembered (in int/denoms): sin(5*_X) -> sin(5*_X) {--> enter int/denoms, args = sin(5*_X) {--> enter int/denoms, args = 5*_X <-- exit int/denoms (now in int/denoms) = {}} {} <-- exit int/denoms (now in int/denoms) = {}} {_X} <-- exit int/denoms (now in int/indef2) = {_X}} denoms := {_X} dummies := {} {--> enter remove, args = depends, {sin(5*_X), 5*_X, _X}, {} {--> enter unknown, args = sin(5*_X), {} {--> enter depends, args = sin(5*_X), {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {--> enter unknown, args = 5*_X, {} {--> enter depends, args = 5*_X, {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {--> enter unknown, args = _X, {} {--> enter depends, args = _X, {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {sin(5 _X), 5 _X, _X} <-- exit remove (now in int/indef2) = {sin(5*_X), 5*_X, _X}} ddset := {sin(5 _X), 5 _X, _X} z := sin(5 _X) {--> enter diff/sin, args = 5*_X, _X {--> enter cos, args = 5*_X {--> enter csgn, args = 5 <-- exit csgn (now in cos) = 1} cos(5 _X) := cos(5 _X) <-- exit cos (now in diff/sin) = cos(5*_X)} 5 cos(5 _X) <-- exit diff/sin (now in int/indef2) = 5*cos(5*_X)} dz := 5 cos(5 _X) _Y t := 1/5 ------------- 5 _X cos(5 _X) z := 5 _X dz := 5 z := _X dz := 1 {--> enter type/indexedfun, args = sin(5*_X), _X false <-- exit type/indexedfun (now in int/indef2) = false} #21 {--> enter int/subs, args = 5*_X, a0, a1, t {--> enter ispoly, args = 5*_X, linear, _X, a0, a1 <-- exit ispoly (now in int/subs) = true} a0 := 5 _X a1 := 1/5 _X t := _X <-- exit int/subs (now in int/indef2) = true} sin(_X) t := 625 ------- 5 _X #22 {--> enter int/indef1, args = 625/_X^5*sin(_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(_X) answer := int/itable[625 -------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 625/_X^5*sin(_X), _X 625 <-- exit remove (now in int/indef1) = 625} c := 625 sin(_X) g := ------- 5 _X #23 {--> enter int/indef1, args = 1/_X^5*sin(_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(_X) answer := int/itable[-------] 5 _X #24 sin(_X) cos(_X) sin(_X) cos(_X) - 1/4 ------- - 1/12 ------- + 1/24 ------- + 1/24 ------- + 1/24 Si(_X) 4 3 2 _X _X _X _X <-- exit int/indef1 (now in int/indef1) = -1/4*sin(_X)/_X^4-1/12*cos(_X)/_X^3+1/24*sin(_X)/_X^2+1/24*cos(_X)/_X+1/24*Si(_X)} sin(_X) cos(_X) sin(_X) cos(_X) r := - 1/4 ------- - 1/12 ------- + 1/24 ------- + 1/24 ------- 4 3 2 _X _X _X _X + 1/24 Si(_X) answer := sin(_X) 625 cos(_X) 625 sin(_X) 625 cos(_X) 625 - 625/4 ------- - --- ------- + --- ------- + --- ------- + --- Si(_X) 4 12 3 24 2 24 _X 24 _X _X _X sin(_X) 625 cos(_X) 625 sin(_X) 625 cos(_X) 625 - 625/4 ------- - --- ------- + --- ------- + --- ------- + --- Si(_X) 4 12 3 24 2 24 _X 24 _X _X _X <-- exit int/indef1 (now in int/indef2) = -625/4*sin(_X)/_X^4-625/12*cos(_X)/_X^3+625/24*sin(_X)/_X^2+625/24*cos(_X)/_X+625/24*Si(_X)} <-- exit int/indef2 (now in int/indef1) = -1/4*sin(5*_X)/_X^4-5/12*cos(5*_X)/_X^3+25/24*sin(5*_X)/_X^2+125/24*cos(5*_X)/_X+625/24*Si(5*_X)} sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) answer := - 1/4 --------- - 5/12 --------- + -- --------- + --- --------- 4 3 24 2 24 _X _X _X _X 625 + --- Si(5 _X) 24 sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) - 1/4 --------- - 5/12 --------- + -- --------- + --- --------- 4 3 24 2 24 _X _X _X _X 625 + --- Si(5 _X) 24 <-- exit int/indef1 (now in int/indef1) = -1/4*sin(5*_X)/_X^4-5/12*cos(5*_X)/_X^3+25/24*sin(5*_X)/_X^2+125/24*cos(5*_X)/_X+625/24*Si(5*_X)} sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) r := - 1/4 --------- - 5/12 --------- + -- --------- + --- --------- 4 3 24 2 24 _X _X _X _X 625 + --- Si(5 _X) 24 sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) answer := - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 + --- Si(5 _X) 384 sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 + --- Si(5 _X) 384 <-- exit int/indef1 (now in int/indef1) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)} #25 {--> enter int/indef1, args = -5/16/_X^5*sin(3*_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(3 _X) answer := int/itable[- 5/16 ---------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, -5/16/_X^5*sin(3*_X), _X {--> enter unknown, args = -5/16, _X true <-- exit unknown (now in remove) = true} {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = sin(3*_X), _X false <-- exit unknown (now in remove) = false} -5 -- 16 <-- exit remove (now in int/indef1) = -5/16} -5 c := -- 16 sin(3 _X) g := --------- 5 _X {--> enter int/indef1, args = 1/_X^5*sin(3*_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(3 _X) answer := int/itable[---------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 1/_X^5*sin(3*_X), _X {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = sin(3*_X), _X false <-- exit unknown (now in remove) = false} 1 <-- exit remove (now in int/indef1) = 1} c := 1 sin(3 _X) g := --------- 5 _X {--> enter type/radfun, args = 1/_X^5*sin(3*_X), anything, _X v := {_X} r := sin(3 _X) <-- exit type/radfun (now in int/indef1) = false} {--> enter int/indef2, args = 1/_X^5*sin(3*_X) {--> enter unknown, args = sin(3*_X) sin(3 _X) <-- exit unknown (now in int/indef2) = sin(3*_X)} {--> enter unknown, args = _X _X <-- exit unknown (now in int/indef2) = _X} inds := {sin(3 _X), _X} {--> enter unknown, args = sin(3*_X) sin(3 _X) <-- exit unknown (now in int/indef2) = sin(3*_X)} {--> enter unknown, args = _X <-- exit unknown (now in int/indef2) = } fcns := {sin(3 _X)} algs := {} bases := {} {--> enter unknown, args = sin(3*_X) 3 _X <-- exit unknown (now in int/indef2) = 3*_X} fargs := {3 _X} {--> enter unknown, args = sin(3*_X) sin <-- exit unknown (now in int/indef2) = sin} fnames := {sin} {--> enter int/denoms, args = 1/_X^5*sin(3*_X) value remembered (in int/denoms): sin(3*_X) -> sin(3*_X) value remembered (in int/denoms): int/denoms(1/_X^5) -> {_X} value remembered (in int/denoms): sin(3*_X) -> sin(3*_X) {--> enter int/denoms, args = sin(3*_X) {--> enter int/denoms, args = 3*_X <-- exit int/denoms (now in int/denoms) = {}} {} <-- exit int/denoms (now in int/denoms) = {}} {_X} <-- exit int/denoms (now in int/indef2) = {_X}} denoms := {_X} dummies := {} {--> enter remove, args = depends, {sin(3*_X), 3*_X, _X}, {} {--> enter unknown, args = sin(3*_X), {} {--> enter depends, args = sin(3*_X), {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {--> enter unknown, args = 3*_X, {} {--> enter depends, args = 3*_X, {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {--> enter unknown, args = _X, {} {--> enter depends, args = _X, {} <-- exit depends (now in unknown) = false} true <-- exit unknown (now in remove) = true} {sin(3 _X), 3 _X, _X} <-- exit remove (now in int/indef2) = {sin(3*_X), 3*_X, _X}} ddset := {sin(3 _X), 3 _X, _X} z := sin(3 _X) {--> enter diff/sin, args = 3*_X, _X {--> enter cos, args = 3*_X {--> enter csgn, args = 3 <-- exit csgn (now in cos) = 1} cos(3 _X) := cos(3 _X) <-- exit cos (now in diff/sin) = cos(3*_X)} 3 cos(3 _X) <-- exit diff/sin (now in int/indef2) = 3*cos(3*_X)} dz := 3 cos(3 _X) _Y t := 1/3 ------------- 5 _X cos(3 _X) z := 3 _X dz := 3 z := _X dz := 1 {--> enter type/indexedfun, args = sin(3*_X), _X false <-- exit type/indexedfun (now in int/indef2) = false} {--> enter int/subs, args = 3*_X, a0, a1, t {--> enter ispoly, args = 3*_X, linear, _X, a0, a1 <-- exit ispoly (now in int/subs) = true} a0 := 3 _X a1 := 1/3 _X t := _X <-- exit int/subs (now in int/indef2) = true} sin(_X) t := 81 ------- 5 _X {--> enter int/indef1, args = 81/_X^5*sin(_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(_X) answer := int/itable[81 -------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 81/_X^5*sin(_X), _X 81 <-- exit remove (now in int/indef1) = 81} c := 81 sin(_X) g := ------- 5 _X sin(_X) cos(_X) sin(_X) cos(_X) r := - 1/4 ------- - 1/12 ------- + 1/24 ------- + 1/24 ------- 4 3 2 _X _X _X _X + 1/24 Si(_X) sin(_X) cos(_X) sin(_X) cos(_X) answer := - 81/4 ------- - 27/4 ------- + 27/8 ------- + 27/8 ------- 4 3 2 _X _X _X _X + 27/8 Si(_X) sin(_X) cos(_X) sin(_X) cos(_X) - 81/4 ------- - 27/4 ------- + 27/8 ------- + 27/8 ------- + 27/8 Si(_X) 4 3 2 _X _X _X _X <-- exit int/indef1 (now in int/indef2) = -81/4*sin(_X)/_X^4-27/4*cos(_X)/_X^3+27/8*sin(_X)/_X^2+27/8*cos(_X)/_X+27/8*Si(_X)} <-- exit int/indef2 (now in int/indef1) = -1/4*sin(3*_X)/_X^4-1/4*cos(3*_X)/_X^3+3/8*sin(3*_X)/_X^2+9/8*cos(3*_X)/_X+27/8*Si(3*_X)} sin(3 _X) cos(3 _X) sin(3 _X) cos(3 _X) answer := - 1/4 --------- - 1/4 --------- + 3/8 --------- + 9/8 --------- 4 3 2 _X _X _X _X + 27/8 Si(3 _X) sin(3 _X) cos(3 _X) sin(3 _X) cos(3 _X) - 1/4 --------- - 1/4 --------- + 3/8 --------- + 9/8 --------- 4 3 2 _X _X _X _X + 27/8 Si(3 _X) <-- exit int/indef1 (now in int/indef1) = -1/4*sin(3*_X)/_X^4-1/4*cos(3*_X)/_X^3+3/8*sin(3*_X)/_X^2+9/8*cos(3*_X)/_X+27/8*Si(3*_X)} sin(3 _X) cos(3 _X) sin(3 _X) cos(3 _X) r := - 1/4 --------- - 1/4 --------- + 3/8 --------- + 9/8 --------- 4 3 2 _X _X _X _X + 27/8 Si(3 _X) sin(3 _X) cos(3 _X) 15 sin(3 _X) 45 cos(3 _X) answer := 5/64 --------- + 5/64 --------- - --- --------- - --- --------- 4 3 128 2 128 _X _X _X _X 135 - --- Si(3 _X) 128 sin(3 _X) cos(3 _X) 15 sin(3 _X) 45 cos(3 _X) 5/64 --------- + 5/64 --------- - --- --------- - --- --------- 4 3 128 2 128 _X _X _X _X 135 - --- Si(3 _X) 128 <-- exit int/indef1 (now in int/indef1) = 5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)} #26 {--> enter int/indef1, args = 5/8/_X^5*sin(_X) table([ _X ----------- = 1 + sin(_X) _X cos(1/2 _X) -2 ------------------------- + _X + 2 ln(sin(1/2 _X) + cos(1/2 _X)) sin(1/2 _X) + cos(1/2 _X) cosh(_X) = sinh(_X) arccosh(_X) = _X arccosh(_X) - sqrt(_X - 1) sqrt(_X + 1) 2 arccot(_X) = arccot(_X) _X + 1/2 ln(_X + 1) cot(_X) = ln(sin(_X)) 1 arccsc(_X) = arccsc(_X) _X + ln(_X + _X sqrt(1 - ---)) 2 _X sqrt(cot(_X)) = sqrt(cot(_X)) sin(_X) sqrt(2) arccos(sin(_X) - cos(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(sin(_X) + sqrt(2) sqrt(cot(_X)) sin(_X) + cos(_X)) sqrt(coth(_X)) = arctanh(sqrt(coth(_X))) - arctan(sqrt(coth(_X))) sqrt(tanh(_X)) = arctanh(sqrt(tanh(_X))) - arctan(sqrt(tanh(_X))) 2 arcsin(_X) = _X arcsin(_X) + sqrt(1 - _X ) _X ----------- = -_X cot(1/2 _X) + 2 ln(sin(1/2 _X)) 1 - cos(_X) _X - sin(_X) ------------ = -_X cot(1/2 _X) 1 - cos(_X) 2 arctan(_X) = _X arctan(_X) - 1/2 ln(_X + 1) exp(_X) = exp(_X) sec(_X) = ln(sec(_X) + tan(_X)) sinh(_X) = cosh(_X) _X + sin(_X) ------------ = _X tan(1/2 _X) 1 + cos(_X) sech(_X) = arctan(sinh(_X)) sin(ln(_X)) = - 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X csch(_X) = ln(tanh(1/2 _X)) tan(_X) = -ln(cos(_X)) sin(_X) = -cos(_X) cos(_X) = sin(_X) 2 arctanh(_X) = _X arctanh(_X) + 1/2 ln(1 - _X ) ln(_X) = _X ln(_X) - _X coth(_X) = ln(sinh(_X)) _X ----------- = _X tan(1/2 _X) + 2 ln(cos(1/2 _X)) 1 + cos(_X) _X ----------- = 1 - sin(_X) _X cos(1/2 _X) 2 -------------------------- - _X + 2 ln(-sin(1/2 _X) + cos(1/2 _X)) -sin(1/2 _X) + cos(1/2 _X) 1 arcsec(_X) = _X arcsec(_X) - ln(_X + _X sqrt(1 - ---)) 2 _X cos(ln(_X)) = 1/2 cos(ln(_X)) _X + 1/2 sin(ln(_X)) _X 1 1 arcsech(_X) = _X arcsech(_X) - arctan(sqrt(---- - 1) sqrt(---- + 1)) _X _X 1 arccsch(_X) = _X arccsch(_X) + ln(_X + _X sqrt(1 + ---)) 2 _X csc(_X) = -ln(csc(_X) + cot(_X)) sqrt(tan(_X)) = sqrt(tan(_X)) cos(_X) sqrt(2) arccos(cos(_X) - sin(_X)) 1/2 ------------------------------------------------------- sqrt(cos(_X) sin(_X)) - 1/2 sqrt(2) ln(cos(_X) + sqrt(2) sqrt(tan(_X)) cos(_X) + sin(_X)) tanh(_X) = ln(cosh(_X)) 2 arcsinh(_X) = _X arcsinh(_X) - sqrt(_X + 1) 2 arccos(_X) = _X arccos(_X) - sqrt(1 - _X ) 2 arccoth(_X) = _X arccoth(_X) + 1/2 ln(_X - 1) ]) sin(_X) answer := int/itable[5/8 -------] 5 _X answer := int/indef1/NOVAL {--> enter remove, args = has, 5/8/_X^5*sin(_X), _X {--> enter unknown, args = 5/8, _X true <-- exit unknown (now in remove) = true} {--> enter unknown, args = 1/_X^5, _X false <-- exit unknown (now in remove) = false} {--> enter unknown, args = sin(_X), _X false <-- exit unknown (now in remove) = false} 5/8 <-- exit remove (now in int/indef1) = 5/8} c := 5/8 sin(_X) g := ------- 5 _X value remembered (in int/indef1): int/indef1(1/_X^5*sin(_X)) -> -1/4*sin(_X)/_X^4-1/12*cos(_X)/_X^3+1/24*sin(_X)/_X^2+1/24*cos(_X)/_X+1/24*Si(_X) sin(_X) cos(_X) sin(_X) cos(_X) r := - 1/4 ------- - 1/12 ------- + 1/24 ------- + 1/24 ------- 4 3 2 _X _X _X _X + 1/24 Si(_X) sin(_X) cos(_X) sin(_X) cos(_X) answer := - 5/32 ------- - 5/96 ------- + 5/192 ------- + 5/192 ------- 4 3 2 _X _X _X _X + 5/192 Si(_X) sin(_X) cos(_X) sin(_X) cos(_X) - 5/32 ------- - 5/96 ------- + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 4 3 2 _X _X _X _X <-- exit int/indef1 (now in int/indef1) = -5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) answer := - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X <-- exit int/indef1 (now in int/xsincos) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)+5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)-5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} <-- exit int/xsincos (now in int/trigon) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)+5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)-5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} <-- exit int/trigon (now in int/indef2) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)+5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)-5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} #27 sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) r := - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X <-- exit int/indef2 (now in int/indef1) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)+5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)-5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) answer := - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X <-- exit int/indef1 (now in int/indef0) = -1/64*sin(5*_X)/_X^4-5/192*cos(5*_X)/_X^3+25/384*sin(5*_X)/_X^2+125/384*cos(5*_X)/_X+625/384*Si(5*_X)+5/64*sin(3*_X)/_X^4+5/64*cos(3*_X)/_X^3-15/128*sin(3*_X)/_X^2-45/128*cos(3*_X)/_X-135/128*Si(3*_X)-5/32*sin(_X)/_X^4-5/96*cos(_X)/_X^3+5/192*sin(_X)/_X^2+5/192*cos(_X)/_X+5/192*Si(_X)} sin(5 _X) cos(5 _X) 25 sin(5 _X) 125 cos(5 _X) answer := - 1/64 --------- - 5/192 --------- + --- --------- + --- --------- 4 3 384 2 384 _X _X _X _X 625 sin(3 _X) cos(3 _X) 15 sin(3 _X) + --- Si(5 _X) + 5/64 --------- + 5/64 --------- - --- --------- 384 4 3 128 2 _X _X _X 45 cos(3 _X) 135 sin(_X) cos(_X) - --- --------- - --- Si(3 _X) - 5/32 ------- - 5/96 ------- 128 _X 128 4 3 _X _X sin(_X) cos(_X) + 5/192 ------- + 5/192 ------- + 5/192 Si(_X) 2 _X _X sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) 625 - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- + --- Si(5 x) 4 3 384 2 384 x 384 x x x sin(3 x) cos(3 x) 15 sin(3 x) 45 cos(3 x) + 5/64 -------- + 5/64 -------- - --- -------- - --- -------- 4 3 128 2 128 x x x x 135 sin(x) cos(x) sin(x) - --- Si(3 x) - 5/32 ------ - 5/96 ------ + 5/192 ------ 128 4 3 2 x x x cos(x) + 5/192 ------ + 5/192 Si(x) x <-- exit int/indef0 (now in int/indefinite) = -1/64*sin(5*x)/x^4-5/192*cos(5*x)/x^3+25/384*sin(5*x)/x^2+125/384*cos(5*x)/x+625/384*Si(5*x)+5/64*sin(3*x)/x^4+5/64*cos(3*x)/x^3-15/128*sin(3*x)/x^2-45/128*cos(3*x)/x-135/128*Si(3*x)-5/32*sin(x)/x^4-5/96*cos(x)/x^3+5/192*sin(x)/x^2+5/192*cos(x)/x+5/192*Si(x)} sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) answer := - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- 4 3 384 2 384 x x x x 625 sin(3 x) cos(3 x) 15 sin(3 x) + --- Si(5 x) + 5/64 -------- + 5/64 -------- - --- -------- 384 4 3 128 2 x x x 45 cos(3 x) 135 sin(x) cos(x) - --- -------- - --- Si(3 x) - 5/32 ------ - 5/96 ------ 128 x 128 4 3 x x sin(x) cos(x) + 5/192 ------ + 5/192 ------ + 5/192 Si(x) 2 x x sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) 625 - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- + --- Si(5 x) 4 3 384 2 384 x 384 x x x sin(3 x) cos(3 x) 15 sin(3 x) 45 cos(3 x) + 5/64 -------- + 5/64 -------- - --- -------- - --- -------- 4 3 128 2 128 x x x x 135 sin(x) cos(x) sin(x) - --- Si(3 x) - 5/32 ------ - 5/96 ------ + 5/192 ------ 128 4 3 2 x x x cos(x) + 5/192 ------ + 5/192 Si(x) x <-- exit int/indefinite (now in int/int) = -1/64*sin(5*x)/x^4-5/192*cos(5*x)/x^3+25/384*sin(5*x)/x^2+125/384*cos(5*x)/x+625/384*Si(5*x)+5/64*sin(3*x)/x^4+5/64*cos(3*x)/x^3-15/128*sin(3*x)/x^2-45/128*cos(3*x)/x-135/128*Si(3*x)-5/32*sin(x)/x^4-5/96*cos(x)/x^3+5/192*sin(x)/x^2+5/192*cos(x)/x+5/192*Si(x)} sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) answer := - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- 4 3 384 2 384 x x x x 625 sin(3 x) cos(3 x) 15 sin(3 x) + --- Si(5 x) + 5/64 -------- + 5/64 -------- - --- -------- 384 4 3 128 2 x x x 45 cos(3 x) 135 sin(x) cos(x) - --- -------- - --- Si(3 x) - 5/32 ------ - 5/96 ------ 128 x 128 4 3 x x sin(x) cos(x) + 5/192 ------ + 5/192 ------ + 5/192 Si(x) 2 x x sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) answer := - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- 4 3 384 2 384 x x x x 625 sin(3 x) cos(3 x) 15 sin(3 x) + --- Si(5 x) + 5/64 -------- + 5/64 -------- - --- -------- 384 4 3 128 2 x x x 45 cos(3 x) 135 sin(x) cos(x) - --- -------- - --- Si(3 x) - 5/32 ------ - 5/96 ------ 128 x 128 4 3 x x sin(x) cos(x) + 5/192 ------ + 5/192 ------ + 5/192 Si(x) 2 x x sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) 625 - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- + --- Si(5 x) 4 3 384 2 384 x 384 x x x sin(3 x) cos(3 x) 15 sin(3 x) 45 cos(3 x) + 5/64 -------- + 5/64 -------- - --- -------- - --- -------- 4 3 128 2 128 x x x x 135 sin(x) cos(x) sin(x) - --- Si(3 x) - 5/32 ------ - 5/96 ------ + 5/192 ------ 128 4 3 2 x x x cos(x) + 5/192 ------ + 5/192 Si(x) x <-- exit int/int (now in int) = -1/64*sin(5*x)/x^4-5/192*cos(5*x)/x^3+25/384*sin(5*x)/x^2+125/384*cos(5*x)/x+625/384*Si(5*x)+5/64*sin(3*x)/x^4+5/64*cos(3*x)/x^3-15/128*sin(3*x)/x^2-45/128*cos(3*x)/x-135/128*Si(3*x)-5/32*sin(x)/x^4-5/96*cos(x)/x^3+5/192*sin(x)/x^2+5/192*cos(x)/x+5/192*Si(x)} sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) answer := - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- 4 3 384 2 384 x x x x 625 sin(3 x) cos(3 x) 15 sin(3 x) + --- Si(5 x) + 5/64 -------- + 5/64 -------- - --- -------- 384 4 3 128 2 x x x 45 cos(3 x) 135 sin(x) cos(x) - --- -------- - --- Si(3 x) - 5/32 ------ - 5/96 ------ 128 x 128 4 3 x x sin(x) cos(x) + 5/192 ------ + 5/192 ------ + 5/192 Si(x) 2 x x sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) 625 - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- + --- Si(5 x) 4 3 384 2 384 x 384 x x x sin(3 x) cos(3 x) 15 sin(3 x) 45 cos(3 x) + 5/64 -------- + 5/64 -------- - --- -------- - --- -------- 4 3 128 2 128 x x x x 135 sin(x) cos(x) sin(x) - --- Si(3 x) - 5/32 ------ - 5/96 ------ + 5/192 ------ 128 4 3 2 x x x cos(x) + 5/192 ------ + 5/192 Si(x) x #28 <-- exit int (now at top level) = -1/64*sin(5*x)/x^4-5/192*cos(5*x)/x^3+25/384*sin(5*x)/x^2+125/384*cos(5*x)/x+625/384*Si(5*x)+5/64*sin(3*x)/x^4+5/64*cos(3*x)/x^3-15/128*sin(3*x)/x^2-45/128*cos(3*x)/x-135/128*Si(3*x)-5/32*sin(x)/x^4-5/96*cos(x)/x^3+5/192*sin(x)/x^2+5/192*cos(x)/x+5/192*Si(x)} sin(5 x) cos(5 x) 25 sin(5 x) 125 cos(5 x) 625 - 1/64 -------- - 5/192 -------- + --- -------- + --- -------- + --- Si(5 x) 4 3 384 2 384 x 384 x x x sin(3 x) cos(3 x) 15 sin(3 x) 45 cos(3 x) + 5/64 -------- + 5/64 -------- - --- -------- - --- -------- 4 3 128 2 128 x x x x 135 sin(x) cos(x) sin(x) - --- Si(3 x) - 5/32 ------ - 5/96 ------ + 5/192 ------ 128 4 3 2 x x x cos(x) + 5/192 ------ + 5/192 Si(x) x > printlevel:=1: > writeto(terminal):