3.58.80 \(\int \frac {(-18-6 x+9 x^2+3 x^3) \log ^2(x) \log (2 x-x^3)+\log ^3(x) (12+4 x-18 x^2-6 x^3+(30+8 x-15 x^2-4 x^3) \log (2 x-x^3))}{(-2 x^6+x^8) \log ^3(2 x-x^3)} \, dx\)

Optimal. Leaf size=23 \[ \frac {(3+x) \log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \]

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Rubi [F]  time = 3.20, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (-18-6 x+9 x^2+3 x^3\right ) \log ^2(x) \log \left (2 x-x^3\right )+\log ^3(x) \left (12+4 x-18 x^2-6 x^3+\left (30+8 x-15 x^2-4 x^3\right ) \log \left (2 x-x^3\right )\right )}{\left (-2 x^6+x^8\right ) \log ^3\left (2 x-x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-18 - 6*x + 9*x^2 + 3*x^3)*Log[x]^2*Log[2*x - x^3] + Log[x]^3*(12 + 4*x - 18*x^2 - 6*x^3 + (30 + 8*x - 1
5*x^2 - 4*x^3)*Log[2*x - x^3]))/((-2*x^6 + x^8)*Log[2*x - x^3]^3),x]

[Out]

Defer[Int][Log[x]^3/((Sqrt[2] - x)*Log[x*(2 - x^2)]^3), x]/2 + (3*Defer[Int][Log[x]^3/((Sqrt[2] - x)*Log[x*(2
- x^2)]^3), x])/(2*Sqrt[2]) - 6*Defer[Int][Log[x]^3/(x^6*Log[x*(2 - x^2)]^3), x] - 2*Defer[Int][Log[x]^3/(x^5*
Log[x*(2 - x^2)]^3), x] + 6*Defer[Int][Log[x]^3/(x^4*Log[x*(2 - x^2)]^3), x] + 2*Defer[Int][Log[x]^3/(x^3*Log[
x*(2 - x^2)]^3), x] + 3*Defer[Int][Log[x]^3/(x^2*Log[x*(2 - x^2)]^3), x] + Defer[Int][Log[x]^3/(x*Log[x*(2 - x
^2)]^3), x] - Defer[Int][Log[x]^3/((Sqrt[2] + x)*Log[x*(2 - x^2)]^3), x]/2 + (3*Defer[Int][Log[x]^3/((Sqrt[2]
+ x)*Log[x*(2 - x^2)]^3), x])/(2*Sqrt[2]) + 9*Defer[Int][Log[x]^2/(x^6*Log[x*(2 - x^2)]^2), x] + 3*Defer[Int][
Log[x]^2/(x^5*Log[x*(2 - x^2)]^2), x] - 15*Defer[Int][Log[x]^3/(x^6*Log[x*(2 - x^2)]^2), x] - 4*Defer[Int][Log
[x]^3/(x^5*Log[x*(2 - x^2)]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-18-6 x+9 x^2+3 x^3\right ) \log ^2(x) \log \left (2 x-x^3\right )+\log ^3(x) \left (12+4 x-18 x^2-6 x^3+\left (30+8 x-15 x^2-4 x^3\right ) \log \left (2 x-x^3\right )\right )}{x^6 \left (-2+x^2\right ) \log ^3\left (2 x-x^3\right )} \, dx\\ &=\int \left (\frac {2 \left (-6-2 x+9 x^2+3 x^3\right ) \log ^3(x)}{x^6 \left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )}+\frac {\log ^2(x) (9+3 x-15 \log (x)-4 x \log (x))}{x^6 \log ^2\left (x \left (2-x^2\right )\right )}\right ) \, dx\\ &=2 \int \frac {\left (-6-2 x+9 x^2+3 x^3\right ) \log ^3(x)}{x^6 \left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx+\int \frac {\log ^2(x) (9+3 x-15 \log (x)-4 x \log (x))}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx\\ &=2 \int \left (-\frac {3 \log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )}-\frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )}+\frac {3 \log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )}+\frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )}+\frac {3 \log ^3(x)}{2 x^2 \log ^3\left (x \left (2-x^2\right )\right )}+\frac {\log ^3(x)}{2 x \log ^3\left (x \left (2-x^2\right )\right )}+\frac {(3+x) \log ^3(x)}{2 \left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )}\right ) \, dx+\int \left (\frac {9 \log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )}+\frac {3 \log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )}-\frac {15 \log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )}-\frac {4 \log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )}\right ) \, dx\\ &=-\left (2 \int \frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )} \, dx\right )+2 \int \frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^3(x)}{x^2 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-4 \int \frac {\log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-6 \int \frac {\log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+6 \int \frac {\log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+9 \int \frac {\log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-15 \int \frac {\log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx+\int \frac {\log ^3(x)}{x \log ^3\left (x \left (2-x^2\right )\right )} \, dx+\int \frac {(3+x) \log ^3(x)}{\left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx\\ &=-\left (2 \int \frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )} \, dx\right )+2 \int \frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^3(x)}{x^2 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-4 \int \frac {\log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-6 \int \frac {\log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+6 \int \frac {\log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+9 \int \frac {\log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-15 \int \frac {\log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx+\int \left (\frac {3 \log ^3(x)}{\left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )}+\frac {x \log ^3(x)}{\left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )}\right ) \, dx+\int \frac {\log ^3(x)}{x \log ^3\left (x \left (2-x^2\right )\right )} \, dx\\ &=-\left (2 \int \frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )} \, dx\right )+2 \int \frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^3(x)}{x^2 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^3(x)}{\left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-4 \int \frac {\log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-6 \int \frac {\log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+6 \int \frac {\log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+9 \int \frac {\log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-15 \int \frac {\log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx+\int \frac {\log ^3(x)}{x \log ^3\left (x \left (2-x^2\right )\right )} \, dx+\int \frac {x \log ^3(x)}{\left (2-x^2\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx\\ &=-\left (2 \int \frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )} \, dx\right )+2 \int \frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \left (\frac {\log ^3(x)}{2 \sqrt {2} \left (\sqrt {2}-x\right ) \log ^3\left (x \left (2-x^2\right )\right )}+\frac {\log ^3(x)}{2 \sqrt {2} \left (\sqrt {2}+x\right ) \log ^3\left (x \left (2-x^2\right )\right )}\right ) \, dx+3 \int \frac {\log ^3(x)}{x^2 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-4 \int \frac {\log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-6 \int \frac {\log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+6 \int \frac {\log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+9 \int \frac {\log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-15 \int \frac {\log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx+\int \left (\frac {\log ^3(x)}{2 \left (\sqrt {2}-x\right ) \log ^3\left (x \left (2-x^2\right )\right )}-\frac {\log ^3(x)}{2 \left (\sqrt {2}+x\right ) \log ^3\left (x \left (2-x^2\right )\right )}\right ) \, dx+\int \frac {\log ^3(x)}{x \log ^3\left (x \left (2-x^2\right )\right )} \, dx\\ &=\frac {1}{2} \int \frac {\log ^3(x)}{\left (\sqrt {2}-x\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx-\frac {1}{2} \int \frac {\log ^3(x)}{\left (\sqrt {2}+x\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx-2 \int \frac {\log ^3(x)}{x^5 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+2 \int \frac {\log ^3(x)}{x^3 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^3(x)}{x^2 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+3 \int \frac {\log ^2(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-4 \int \frac {\log ^3(x)}{x^5 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-6 \int \frac {\log ^3(x)}{x^6 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+6 \int \frac {\log ^3(x)}{x^4 \log ^3\left (x \left (2-x^2\right )\right )} \, dx+9 \int \frac {\log ^2(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx-15 \int \frac {\log ^3(x)}{x^6 \log ^2\left (x \left (2-x^2\right )\right )} \, dx+\frac {3 \int \frac {\log ^3(x)}{\left (\sqrt {2}-x\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx}{2 \sqrt {2}}+\frac {3 \int \frac {\log ^3(x)}{\left (\sqrt {2}+x\right ) \log ^3\left (x \left (2-x^2\right )\right )} \, dx}{2 \sqrt {2}}+\int \frac {\log ^3(x)}{x \log ^3\left (x \left (2-x^2\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 22, normalized size = 0.96 \begin {gather*} \frac {(3+x) \log ^3(x)}{x^5 \log ^2\left (-x \left (-2+x^2\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-18 - 6*x + 9*x^2 + 3*x^3)*Log[x]^2*Log[2*x - x^3] + Log[x]^3*(12 + 4*x - 18*x^2 - 6*x^3 + (30 + 8
*x - 15*x^2 - 4*x^3)*Log[2*x - x^3]))/((-2*x^6 + x^8)*Log[2*x - x^3]^3),x]

[Out]

((3 + x)*Log[x]^3)/(x^5*Log[-(x*(-2 + x^2))]^2)

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fricas [A]  time = 0.53, size = 23, normalized size = 1.00 \begin {gather*} \frac {{\left (x + 3\right )} \log \relax (x)^{3}}{x^{5} \log \left (-x^{3} + 2 \, x\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-15*x^2+8*x+30)*log(-x^3+2*x)-6*x^3-18*x^2+4*x+12)*log(x)^3+(3*x^3+9*x^2-6*x-18)*log(-x^3+2
*x)*log(x)^2)/(x^8-2*x^6)/log(-x^3+2*x)^3,x, algorithm="fricas")

[Out]

(x + 3)*log(x)^3/(x^5*log(-x^3 + 2*x)^2)

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giac [B]  time = 0.24, size = 114, normalized size = 4.96 \begin {gather*} \frac {3 \, x^{3} \log \relax (x)^{3} + 9 \, x^{2} \log \relax (x)^{3} - 2 \, x \log \relax (x)^{3} - 6 \, \log \relax (x)^{3}}{3 \, x^{7} \log \left (-x^{2} + 2\right )^{2} + 6 \, x^{7} \log \left (-x^{2} + 2\right ) \log \relax (x) + 3 \, x^{7} \log \relax (x)^{2} - 2 \, x^{5} \log \left (-x^{2} + 2\right )^{2} - 4 \, x^{5} \log \left (-x^{2} + 2\right ) \log \relax (x) - 2 \, x^{5} \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-15*x^2+8*x+30)*log(-x^3+2*x)-6*x^3-18*x^2+4*x+12)*log(x)^3+(3*x^3+9*x^2-6*x-18)*log(-x^3+2
*x)*log(x)^2)/(x^8-2*x^6)/log(-x^3+2*x)^3,x, algorithm="giac")

[Out]

(3*x^3*log(x)^3 + 9*x^2*log(x)^3 - 2*x*log(x)^3 - 6*log(x)^3)/(3*x^7*log(-x^2 + 2)^2 + 6*x^7*log(-x^2 + 2)*log
(x) + 3*x^7*log(x)^2 - 2*x^5*log(-x^2 + 2)^2 - 4*x^5*log(-x^2 + 2)*log(x) - 2*x^5*log(x)^2)

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maple [C]  time = 0.38, size = 138, normalized size = 6.00

method	result	size
risch	\(\frac {4 \left (3+x \right ) \ln \relax (x )^{3}}{x^{5} \left (2 i \pi +2 \ln \relax (x )+2 \ln \left (x^{2}-2\right )+i \pi \mathrm {csgn}\left (i x \left (x^{2}-2\right )\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \left (x^{2}-2\right )\right )^{2} \mathrm {csgn}\left (i \left (x^{2}-2\right )\right )-i \pi \,\mathrm {csgn}\left (i x \left (x^{2}-2\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x^{2}-2\right )\right )+i \pi \mathrm {csgn}\left (i x \left (x^{2}-2\right )\right )^{3}-2 i \pi \mathrm {csgn}\left (i x \left (x^{2}-2\right )\right )^{2}\right )^{2}}\)	\(138\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^3-15*x^2+8*x+30)*ln(-x^3+2*x)-6*x^3-18*x^2+4*x+12)*ln(x)^3+(3*x^3+9*x^2-6*x-18)*ln(-x^3+2*x)*ln(x)
^2)/(x^8-2*x^6)/ln(-x^3+2*x)^3,x,method=_RETURNVERBOSE)

[Out]

4*(3+x)*ln(x)^3/x^5/(2*I*Pi+2*ln(x)+2*ln(x^2-2)+I*Pi*csgn(I*x*(x^2-2))^2*csgn(I*x)+I*Pi*csgn(I*x*(x^2-2))^2*cs
gn(I*(x^2-2))-I*Pi*csgn(I*x*(x^2-2))*csgn(I*x)*csgn(I*(x^2-2))+I*Pi*csgn(I*x*(x^2-2))^3-2*I*Pi*csgn(I*x*(x^2-2
))^2)^2

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maxima [B]  time = 0.42, size = 48, normalized size = 2.09 \begin {gather*} \frac {{\left (x + 3\right )} \log \relax (x)^{3}}{x^{5} \log \left (-x^{2} + 2\right )^{2} + 2 \, x^{5} \log \left (-x^{2} + 2\right ) \log \relax (x) + x^{5} \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-15*x^2+8*x+30)*log(-x^3+2*x)-6*x^3-18*x^2+4*x+12)*log(x)^3+(3*x^3+9*x^2-6*x-18)*log(-x^3+2
*x)*log(x)^2)/(x^8-2*x^6)/log(-x^3+2*x)^3,x, algorithm="maxima")

[Out]

(x + 3)*log(x)^3/(x^5*log(-x^2 + 2)^2 + 2*x^5*log(-x^2 + 2)*log(x) + x^5*log(x)^2)

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mupad [B]  time = 4.89, size = 467, normalized size = 20.30 \begin {gather*} \frac {\frac {{\ln \relax (x)}^3\,\left (x+3\right )}{x^5}-\frac {\ln \left (2\,x-x^3\right )\,{\ln \relax (x)}^2\,\left (x^2-2\right )\,\left (3\,x-15\,\ln \relax (x)-4\,x\,\ln \relax (x)+9\right )}{2\,x^5\,\left (3\,x^2-2\right )}}{{\ln \left (2\,x-x^3\right )}^2}+\frac {\frac {\left (x^2-2\right )\,\left (3\,x\,{\ln \relax (x)}^2-4\,x\,{\ln \relax (x)}^3+9\,{\ln \relax (x)}^2-15\,{\ln \relax (x)}^3\right )}{2\,x^5\,\left (3\,x^2-2\right )}-\frac {\ln \left (2\,x-x^3\right )\,\left (x^2-2\right )\,\left (48\,x^5\,{\ln \relax (x)}^3-72\,x^5\,{\ln \relax (x)}^2+18\,x^5\,\ln \relax (x)+225\,x^4\,{\ln \relax (x)}^3-270\,x^4\,{\ln \relax (x)}^2+54\,x^4\,\ln \relax (x)-160\,x^3\,{\ln \relax (x)}^3+216\,x^3\,{\ln \relax (x)}^2-48\,x^3\,\ln \relax (x)-720\,x^2\,{\ln \relax (x)}^3+792\,x^2\,{\ln \relax (x)}^2-144\,x^2\,\ln \relax (x)+64\,x\,{\ln \relax (x)}^3-96\,x\,{\ln \relax (x)}^2+24\,x\,\ln \relax (x)+300\,{\ln \relax (x)}^3-360\,{\ln \relax (x)}^2+72\,\ln \relax (x)\right )}{2\,x^5\,{\left (3\,x^2-2\right )}^3}}{\ln \left (2\,x-x^3\right )}-\frac {{\ln \relax (x)}^2\,\left (-\frac {4\,x^7}{3}-5\,x^6+\frac {20\,x^5}{3}+\frac {74\,x^4}{3}-\frac {88\,x^3}{9}-36\,x^2+\frac {32\,x}{9}+\frac {40}{3}\right )}{-x^{11}+2\,x^9-\frac {4\,x^7}{3}+\frac {8\,x^5}{27}}+\frac {{\ln \relax (x)}^3\,\left (-\frac {8\,x^7}{9}-\frac {25\,x^6}{6}+\frac {128\,x^5}{27}+\frac {65\,x^4}{3}-\frac {64\,x^3}{9}-\frac {290\,x^2}{9}+\frac {64\,x}{27}+\frac {100}{9}\right )}{-x^{11}+2\,x^9-\frac {4\,x^7}{3}+\frac {8\,x^5}{27}}+\frac {\ln \relax (x)\,\left (\frac {x^5}{3}+x^4-\frac {4\,x^3}{3}-4\,x^2+\frac {4\,x}{3}+4\right )}{x^9-\frac {4\,x^7}{3}+\frac {4\,x^5}{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)^3*(4*x - 18*x^2 - 6*x^3 + log(2*x - x^3)*(8*x - 15*x^2 - 4*x^3 + 30) + 12) - log(2*x - x^3)*log(x
)^2*(6*x - 9*x^2 - 3*x^3 + 18))/(log(2*x - x^3)^3*(2*x^6 - x^8)),x)

[Out]

((log(x)^3*(x + 3))/x^5 - (log(2*x - x^3)*log(x)^2*(x^2 - 2)*(3*x - 15*log(x) - 4*x*log(x) + 9))/(2*x^5*(3*x^2
- 2)))/log(2*x - x^3)^2 + (((x^2 - 2)*(3*x*log(x)^2 - 4*x*log(x)^3 + 9*log(x)^2 - 15*log(x)^3))/(2*x^5*(3*x^2
- 2)) - (log(2*x - x^3)*(x^2 - 2)*(72*log(x) - 96*x*log(x)^2 - 144*x^2*log(x) + 64*x*log(x)^3 - 48*x^3*log(x)
+ 54*x^4*log(x) + 18*x^5*log(x) - 360*log(x)^2 + 300*log(x)^3 + 792*x^2*log(x)^2 - 720*x^2*log(x)^3 + 216*x^3
*log(x)^2 - 160*x^3*log(x)^3 - 270*x^4*log(x)^2 + 225*x^4*log(x)^3 - 72*x^5*log(x)^2 + 48*x^5*log(x)^3 + 24*x*
log(x)))/(2*x^5*(3*x^2 - 2)^3))/log(2*x - x^3) - (log(x)^2*((32*x)/9 - 36*x^2 - (88*x^3)/9 + (74*x^4)/3 + (20*
x^5)/3 - 5*x^6 - (4*x^7)/3 + 40/3))/((8*x^5)/27 - (4*x^7)/3 + 2*x^9 - x^11) + (log(x)^3*((64*x)/27 - (290*x^2)
/9 - (64*x^3)/9 + (65*x^4)/3 + (128*x^5)/27 - (25*x^6)/6 - (8*x^7)/9 + 100/9))/((8*x^5)/27 - (4*x^7)/3 + 2*x^9
- x^11) + (log(x)*((4*x)/3 - 4*x^2 - (4*x^3)/3 + x^4 + x^5/3 + 4))/((4*x^5)/9 - (4*x^7)/3 + x^9)

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sympy [A]  time = 0.31, size = 26, normalized size = 1.13 \begin {gather*} \frac {x \log {\relax (x )}^{3} + 3 \log {\relax (x )}^{3}}{x^{5} \log {\left (- x^{3} + 2 x \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**3-15*x**2+8*x+30)*ln(-x**3+2*x)-6*x**3-18*x**2+4*x+12)*ln(x)**3+(3*x**3+9*x**2-6*x-18)*ln(-
x**3+2*x)*ln(x)**2)/(x**8-2*x**6)/ln(-x**3+2*x)**3,x)

[Out]

(x*log(x)**3 + 3*log(x)**3)/(x**5*log(-x**3 + 2*x)**2)

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