3.78.17 \(\int \frac {(8 x^2-4 e^x x^3-4 x^5+(-16 x^2-6 x^3+8 x^5+e^x (-2 x-2 x^2+8 x^3)) \log (4 x)+(-4+2 e^x x+2 x^3) \log (2-e^x x-x^3)) \log (\frac {\log (4 x)}{-2 x^2+\log (2-e^x x-x^3)})}{(4 x^3-2 e^x x^4-2 x^6) \log (4 x)+(-2 x+e^x x^2+x^4) \log (4 x) \log (2-e^x x-x^3)} \, dx\)

Optimal. Leaf size=33 \[ \log ^2\left (\frac {\log (4 x)}{-2 x^2+\log \left (2-x^2 \left (\frac {e^x}{x}+x\right )\right )}\right ) \]

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Rubi [F]  time = 10.10, 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 (8 x^2-4 e^x x^3-4 x^5+\left (-16 x^2-6 x^3+8 x^5+e^x \left (-2 x-2 x^2+8 x^3\right )\right ) \log (4 x)+\left (-4+2 e^x x+2 x^3\right ) \log \left (2-e^x x-x^3\right )\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (4 x^3-2 e^x x^4-2 x^6\right ) \log (4 x)+\left (-2 x+e^x x^2+x^4\right ) \log (4 x) \log \left (2-e^x x-x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((8*x^2 - 4*E^x*x^3 - 4*x^5 + (-16*x^2 - 6*x^3 + 8*x^5 + E^x*(-2*x - 2*x^2 + 8*x^3))*Log[4*x] + (-4 + 2*E^
x*x + 2*x^3)*Log[2 - E^x*x - x^3])*Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/((4*x^3 - 2*E^x*x^4 - 2*x^6)
*Log[4*x] + (-2*x + E^x*x^2 + x^4)*Log[4*x]*Log[2 - E^x*x - x^3]),x]

[Out]

2*Defer[Int][Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])]/(2*x^2 - Log[2 - E^x*x - x^3]), x] + 2*Defer[Int][L
og[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])]/(x*(2*x^2 - Log[2 - E^x*x - x^3])), x] - 8*Defer[Int][(x*Log[Log[
4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/(2*x^2 - Log[2 - E^x*x - x^3]), x] + 4*Defer[Int][Log[Log[4*x]/(-2*x^2
+ Log[2 - E^x*x - x^3])]/((-2 + E^x*x + x^3)*(2*x^2 - Log[2 - E^x*x - x^3])), x] + 4*Defer[Int][Log[Log[4*x]/(
-2*x^2 + Log[2 - E^x*x - x^3])]/(x*(-2 + E^x*x + x^3)*(2*x^2 - Log[2 - E^x*x - x^3])), x] + 4*Defer[Int][(x^2*
Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/((-2 + E^x*x + x^3)*(2*x^2 - Log[2 - E^x*x - x^3])), x] - 2*Def
er[Int][(x^3*Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/((-2 + E^x*x + x^3)*(2*x^2 - Log[2 - E^x*x - x^3])
), x] + 4*Defer[Int][(x*Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/(Log[4*x]*(2*x^2 - Log[2 - E^x*x - x^3]
)), x] - 2*Defer[Int][(Log[2 - E^x*x - x^3]*Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/(x*Log[4*x]*(2*x^2
- Log[2 - E^x*x - x^3])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int 2 \left (\frac {1}{x \log (4 x)}+\frac {e^x \left (1+x-4 x^2\right )+x \left (8+3 x-4 x^3\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right ) \, dx\\ &=2 \int \left (\frac {1}{x \log (4 x)}+\frac {e^x \left (1+x-4 x^2\right )+x \left (8+3 x-4 x^3\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right ) \, dx\\ &=2 \int \left (-\frac {\left (-2-2 x-2 x^3+x^4\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}-\frac {\left (-2 x^2-\log (4 x)-x \log (4 x)+4 x^2 \log (4 x)+\log \left (2-e^x x-x^3\right )\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}\right ) \, dx\\ &=-\left (2 \int \frac {\left (-2-2 x-2 x^3+x^4\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx\right )-2 \int \frac {\left (-2 x^2-\log (4 x)-x \log (4 x)+4 x^2 \log (4 x)+\log \left (2-e^x x-x^3\right )\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx\\ &=-\left (2 \int \left (-\frac {2 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}-\frac {2 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}-\frac {2 x^2 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}+\frac {x^3 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}\right ) \, dx\right )-2 \int \left (-\frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{2 x^2-\log \left (2-e^x x-x^3\right )}-\frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}+\frac {4 x \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{2 x^2-\log \left (2-e^x x-x^3\right )}-\frac {2 x \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}+\frac {\log \left (2-e^x x-x^3\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )}\right ) \, dx\\ &=2 \int \frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{2 x^2-\log \left (2-e^x x-x^3\right )} \, dx+2 \int \frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx-2 \int \frac {x^3 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx-2 \int \frac {\log \left (2-e^x x-x^3\right ) \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx+4 \int \frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx+4 \int \frac {\log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{x \left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx+4 \int \frac {x^2 \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\left (-2+e^x x+x^3\right ) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx+4 \int \frac {x \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{\log (4 x) \left (2 x^2-\log \left (2-e^x x-x^3\right )\right )} \, dx-8 \int \frac {x \log \left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right )}{2 x^2-\log \left (2-e^x x-x^3\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.17, size = 30, normalized size = 0.91 \begin {gather*} \log ^2\left (\frac {\log (4 x)}{-2 x^2+\log \left (2-e^x x-x^3\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((8*x^2 - 4*E^x*x^3 - 4*x^5 + (-16*x^2 - 6*x^3 + 8*x^5 + E^x*(-2*x - 2*x^2 + 8*x^3))*Log[4*x] + (-4
+ 2*E^x*x + 2*x^3)*Log[2 - E^x*x - x^3])*Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])])/((4*x^3 - 2*E^x*x^4 -
2*x^6)*Log[4*x] + (-2*x + E^x*x^2 + x^4)*Log[4*x]*Log[2 - E^x*x - x^3]),x]

[Out]

Log[Log[4*x]/(-2*x^2 + Log[2 - E^x*x - x^3])]^2

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fricas [A]  time = 1.07, size = 32, normalized size = 0.97 \begin {gather*} \log \left (-\frac {\log \left (4 \, x\right )}{2 \, x^{2} - \log \left (-x^{3} - x e^{x} + 2\right )}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x+2*x^3-4)*log(-exp(x)*x-x^3+2)+((8*x^3-2*x^2-2*x)*exp(x)+8*x^5-6*x^3-16*x^2)*log(4*x)-4*
exp(x)*x^3-4*x^5+8*x^2)*log(log(4*x)/(log(-exp(x)*x-x^3+2)-2*x^2))/((exp(x)*x^2+x^4-2*x)*log(4*x)*log(-exp(x)*
x-x^3+2)+(-2*exp(x)*x^4-2*x^6+4*x^3)*log(4*x)),x, algorithm="fricas")

[Out]

log(-log(4*x)/(2*x^2 - log(-x^3 - x*e^x + 2)))^2

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giac [B]  time = 0.89, size = 119, normalized size = 3.61 \begin {gather*} \log \left (2 \, x^{2} - \log \left (-x^{3} - x e^{x} + 2\right )\right )^{2} - 2 \, \log \left (-2 \, x^{2} + \log \left (-x^{3} - x e^{x} + 2\right )\right ) \log \left (-\log \left (4 \, x\right )\right ) + \log \left (-\log \left (4 \, x\right )\right )^{2} - 2 \, \log \left (2 \, x^{2} - \log \left (-x^{3} - x e^{x} + 2\right )\right ) \log \left (\log \left (4 \, x\right )\right ) + 2 \, \log \left (-2 \, x^{2} + \log \left (-x^{3} - x e^{x} + 2\right )\right ) \log \left (\log \left (4 \, x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x+2*x^3-4)*log(-exp(x)*x-x^3+2)+((8*x^3-2*x^2-2*x)*exp(x)+8*x^5-6*x^3-16*x^2)*log(4*x)-4*
exp(x)*x^3-4*x^5+8*x^2)*log(log(4*x)/(log(-exp(x)*x-x^3+2)-2*x^2))/((exp(x)*x^2+x^4-2*x)*log(4*x)*log(-exp(x)*
x-x^3+2)+(-2*exp(x)*x^4-2*x^6+4*x^3)*log(4*x)),x, algorithm="giac")

[Out]

log(2*x^2 - log(-x^3 - x*e^x + 2))^2 - 2*log(-2*x^2 + log(-x^3 - x*e^x + 2))*log(-log(4*x)) + log(-log(4*x))^2
- 2*log(2*x^2 - log(-x^3 - x*e^x + 2))*log(log(4*x)) + 2*log(-2*x^2 + log(-x^3 - x*e^x + 2))*log(log(4*x))

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maple [C]  time = 0.35, size = 727, normalized size = 22.03

method	result	size
risch	\(\ln \left (x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}\right )^{2}-2 \ln \left (x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}\right ) \ln \left (\ln \left (4 x \right )\right )+\ln \left (\ln \left (4 x \right )\right )^{2}+i \pi \ln \left (\ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}+i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right ) \mathrm {csgn}\left (i \ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )+i \pi \ln \left (\ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{3}-2 i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right )-2 i \pi \ln \left (\ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}-i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{3}+2 i \pi \ln \left (\ln \left (4 x \right )\right )+2 i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}-i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \mathrm {csgn}\left (i \ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}-i \pi \ln \left (\ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right ) \mathrm {csgn}\left (i \ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )-i \pi \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}+i \pi \ln \left (\ln \left (4 x \right )\right ) \mathrm {csgn}\left (i \ln \left (4 x \right )\right ) \mathrm {csgn}\left (\frac {i \ln \left (4 x \right )}{x^{2}-\frac {\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )}{2}}\right )^{2}+2 \ln \left (\ln \left (-{\mathrm e}^{x} x -x^{3}+2\right )-2 x^{2}\right ) \ln \relax (2)-2 \ln \relax (2) \ln \left (\ln \left (4 x \right )\right )\)	\(727\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*exp(x)*x+2*x^3-4)*ln(-exp(x)*x-x^3+2)+((8*x^3-2*x^2-2*x)*exp(x)+8*x^5-6*x^3-16*x^2)*ln(4*x)-4*exp(x)*x
^3-4*x^5+8*x^2)*ln(ln(4*x)/(ln(-exp(x)*x-x^3+2)-2*x^2))/((exp(x)*x^2+x^4-2*x)*ln(4*x)*ln(-exp(x)*x-x^3+2)+(-2*
exp(x)*x^4-2*x^6+4*x^3)*ln(4*x)),x,method=_RETURNVERBOSE)

[Out]

ln(x^2-1/2*ln(-exp(x)*x-x^3+2))^2-2*ln(x^2-1/2*ln(-exp(x)*x-x^3+2))*ln(ln(4*x))+ln(ln(4*x))^2+I*Pi*ln(ln(4*x))
*csgn(I/(x^2-1/2*ln(-exp(x)*x-x^3+2)))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp(x)*x-x^3+2)))^2+I*Pi*ln(ln(-exp(x)*x-x^
3+2)-2*x^2)*csgn(I/(x^2-1/2*ln(-exp(x)*x-x^3+2)))*csgn(I*ln(4*x))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp(x)*x-x^3+2))
)+I*Pi*ln(ln(4*x))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp(x)*x-x^3+2)))^3-2*I*Pi*ln(ln(-exp(x)*x-x^3+2)-2*x^2)-2*I*Pi
*ln(ln(4*x))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp(x)*x-x^3+2)))^2-I*Pi*ln(ln(-exp(x)*x-x^3+2)-2*x^2)*csgn(I*ln(4*x)
/(x^2-1/2*ln(-exp(x)*x-x^3+2)))^3+2*I*Pi*ln(ln(4*x))+2*I*Pi*ln(ln(-exp(x)*x-x^3+2)-2*x^2)*csgn(I*ln(4*x)/(x^2-
1/2*ln(-exp(x)*x-x^3+2)))^2-I*Pi*ln(ln(-exp(x)*x-x^3+2)-2*x^2)*csgn(I*ln(4*x))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp
(x)*x-x^3+2)))^2-I*Pi*ln(ln(4*x))*csgn(I/(x^2-1/2*ln(-exp(x)*x-x^3+2)))*csgn(I*ln(4*x))*csgn(I*ln(4*x)/(x^2-1/
2*ln(-exp(x)*x-x^3+2)))-I*Pi*ln(ln(-exp(x)*x-x^3+2)-2*x^2)*csgn(I/(x^2-1/2*ln(-exp(x)*x-x^3+2)))*csgn(I*ln(4*x
)/(x^2-1/2*ln(-exp(x)*x-x^3+2)))^2+I*Pi*ln(ln(4*x))*csgn(I*ln(4*x))*csgn(I*ln(4*x)/(x^2-1/2*ln(-exp(x)*x-x^3+2
)))^2+2*ln(ln(-exp(x)*x-x^3+2)-2*x^2)*ln(2)-2*ln(2)*ln(ln(4*x))

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maxima [B]  time = 0.54, size = 130, normalized size = 3.94 \begin {gather*} -\log \left (-2 \, x^{2} + \log \left (-x^{3} - x e^{x} + 2\right )\right )^{2} - 2 \, {\left (\log \left (-2 \, x^{2} + \log \left (-x^{3} - x e^{x} + 2\right )\right ) - \log \left (2 \, \log \relax (2) + \log \relax (x)\right )\right )} \log \left (-\frac {\log \left (4 \, x\right )}{2 \, x^{2} - \log \left (-x^{3} - x e^{x} + 2\right )}\right ) + 2 \, \log \left (-2 \, x^{2} + \log \left (-x^{3} - x e^{x} + 2\right )\right ) \log \left (2 \, \log \relax (2) + \log \relax (x)\right ) - \log \left (2 \, \log \relax (2) + \log \relax (x)\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x+2*x^3-4)*log(-exp(x)*x-x^3+2)+((8*x^3-2*x^2-2*x)*exp(x)+8*x^5-6*x^3-16*x^2)*log(4*x)-4*
exp(x)*x^3-4*x^5+8*x^2)*log(log(4*x)/(log(-exp(x)*x-x^3+2)-2*x^2))/((exp(x)*x^2+x^4-2*x)*log(4*x)*log(-exp(x)*
x-x^3+2)+(-2*exp(x)*x^4-2*x^6+4*x^3)*log(4*x)),x, algorithm="maxima")

[Out]

-log(-2*x^2 + log(-x^3 - x*e^x + 2))^2 - 2*(log(-2*x^2 + log(-x^3 - x*e^x + 2)) - log(2*log(2) + log(x)))*log(
-log(4*x)/(2*x^2 - log(-x^3 - x*e^x + 2))) + 2*log(-2*x^2 + log(-x^3 - x*e^x + 2))*log(2*log(2) + log(x)) - lo
g(2*log(2) + log(x))^2

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mupad [B]  time = 6.08, size = 29, normalized size = 0.88 \begin {gather*} {\ln \left (\frac {\ln \left (4\,x\right )}{\ln \left (2-x^3-x\,{\mathrm {e}}^x\right )-2\,x^2}\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(4*x)/(log(2 - x^3 - x*exp(x)) - 2*x^2))*(4*x^3*exp(x) - log(2 - x^3 - x*exp(x))*(2*x*exp(x) + 2*x
^3 - 4) + log(4*x)*(16*x^2 + 6*x^3 - 8*x^5 + exp(x)*(2*x + 2*x^2 - 8*x^3)) - 8*x^2 + 4*x^5))/(log(4*x)*(2*x^4*
exp(x) - 4*x^3 + 2*x^6) - log(4*x)*log(2 - x^3 - x*exp(x))*(x^2*exp(x) - 2*x + x^4)),x)

[Out]

log(log(4*x)/(log(2 - x^3 - x*exp(x)) - 2*x^2))^2

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x+2*x**3-4)*ln(-exp(x)*x-x**3+2)+((8*x**3-2*x**2-2*x)*exp(x)+8*x**5-6*x**3-16*x**2)*ln(4*
x)-4*exp(x)*x**3-4*x**5+8*x**2)*ln(ln(4*x)/(ln(-exp(x)*x-x**3+2)-2*x**2))/((exp(x)*x**2+x**4-2*x)*ln(4*x)*ln(-
exp(x)*x-x**3+2)+(-2*exp(x)*x**4-2*x**6+4*x**3)*ln(4*x)),x)

[Out]

Timed out

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