3.91.66 \(\int \frac {-e^{2 x} x^4+2 \log (x)+(-4-2 x) \log ^2(x)+(-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)) \log (\frac {e^{-2 x} (6 e^{2 x} x^4-e^{2 x} x^4 \log (x)+\log ^2(x))}{x^4})}{6 e^{2 x} x^6-e^{2 x} x^6 \log (x)+x^2 \log ^2(x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {\log \left (6-\log (x)+\frac {e^{-2 x} \left (1-\frac {x+\log (x)}{x}\right )^2}{x^2}\right )}{x} \]

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Rubi [F]  time = 8.93, 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 {-e^{2 x} x^4+2 \log (x)+(-4-2 x) \log ^2(x)+\left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right ) \log \left (\frac {e^{-2 x} \left (6 e^{2 x} x^4-e^{2 x} x^4 \log (x)+\log ^2(x)\right )}{x^4}\right )}{6 e^{2 x} x^6-e^{2 x} x^6 \log (x)+x^2 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

ExpIntegralEi[6 - Log[x]]/E^6 + 12*Defer[Int][Log[x]/(x^2*(-6 + Log[x])*(-6*E^(2*x)*x^4 + E^(2*x)*x^4*Log[x] -
Log[x]^2)), x] - 25*Defer[Int][Log[x]^2/(x^2*(-6 + Log[x])*(-6*E^(2*x)*x^4 + E^(2*x)*x^4*Log[x] - Log[x]^2)),
x] - 12*Defer[Int][Log[x]^2/(x*(-6 + Log[x])*(-6*E^(2*x)*x^4 + E^(2*x)*x^4*Log[x] - Log[x]^2)), x] + 4*Defer[
Int][Log[x]^3/(x^2*(-6 + Log[x])*(-6*E^(2*x)*x^4 + E^(2*x)*x^4*Log[x] - Log[x]^2)), x] + 2*Defer[Int][Log[x]^3
/(x*(-6 + Log[x])*(-6*E^(2*x)*x^4 + E^(2*x)*x^4*Log[x] - Log[x]^2)), x] - Defer[Int][Log[6 - Log[x] + Log[x]^2
/(E^(2*x)*x^4)]/x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\log (x) \left (12-25 \log (x)-12 x \log (x)+4 \log ^2(x)+2 x \log ^2(x)\right )}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}+\frac {1+6 \log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )-\log (x) \log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2 (-6+\log (x))}\right ) \, dx\\ &=\int \frac {\log (x) \left (12-25 \log (x)-12 x \log (x)+4 \log ^2(x)+2 x \log ^2(x)\right )}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+\int \frac {1+6 \log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )-\log (x) \log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2 (-6+\log (x))} \, dx\\ &=\int \left (\frac {12 \log (x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}-\frac {25 \log ^2(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}-\frac {12 \log ^2(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}+\frac {4 \log ^3(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}+\frac {2 \log ^3(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )}\right ) \, dx+\int \frac {\frac {1}{-6+\log (x)}-\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2} \, dx\\ &=2 \int \frac {\log ^3(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+4 \int \frac {\log ^3(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+12 \int \frac {\log (x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-12 \int \frac {\log ^2(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-25 \int \frac {\log ^2(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+\int \left (\frac {1}{x^2 (-6+\log (x))}-\frac {\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {\log ^3(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+4 \int \frac {\log ^3(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+12 \int \frac {\log (x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-12 \int \frac {\log ^2(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-25 \int \frac {\log ^2(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+\int \frac {1}{x^2 (-6+\log (x))} \, dx-\int \frac {\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2} \, dx\\ &=2 \int \frac {\log ^3(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+4 \int \frac {\log ^3(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+12 \int \frac {\log (x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-12 \int \frac {\log ^2(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-25 \int \frac {\log ^2(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-\int \frac {\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2} \, dx+\operatorname {Subst}\left (\int \frac {e^{-x}}{-6+x} \, dx,x,\log (x)\right )\\ &=\frac {\text {Ei}(6-\log (x))}{e^6}+2 \int \frac {\log ^3(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+4 \int \frac {\log ^3(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx+12 \int \frac {\log (x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-12 \int \frac {\log ^2(x)}{x (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-25 \int \frac {\log ^2(x)}{x^2 (-6+\log (x)) \left (-6 e^{2 x} x^4+e^{2 x} x^4 \log (x)-\log ^2(x)\right )} \, dx-\int \frac {\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 26, normalized size = 0.79 \begin {gather*} 2+\frac {\log \left (6-\log (x)+\frac {e^{-2 x} \log ^2(x)}{x^4}\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

2 + Log[6 - Log[x] + Log[x]^2/(E^(2*x)*x^4)]/x

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fricas [A]  time = 0.75, size = 40, normalized size = 1.21 \begin {gather*} \frac {\log \left (-\frac {{\left (x^{4} e^{\left (2 \, x\right )} \log \relax (x) - 6 \, x^{4} e^{\left (2 \, x\right )} - \log \relax (x)^{2}\right )} e^{\left (-2 \, x\right )}}{x^{4}}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(x)^2+x^4*exp(x)^2*log(x)-6*exp(x)^2*x^4)*log((log(x)^2-x^4*exp(x)^2*log(x)+6*exp(x)^2*x^4)/ex
p(x)^2/x^4)+(-2*x-4)*log(x)^2+2*log(x)-exp(x)^2*x^4)/(x^2*log(x)^2-x^6*exp(x)^2*log(x)+6*x^6*exp(x)^2),x, algo
rithm="fricas")

[Out]

log(-(x^4*e^(2*x)*log(x) - 6*x^4*e^(2*x) - log(x)^2)*e^(-2*x)/x^4)/x

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giac [A]  time = 0.37, size = 42, normalized size = 1.27 \begin {gather*} \frac {\log \left (-{\left (x^{4} e^{\left (2 \, x\right )} \log \relax (x) - 6 \, x^{4} e^{\left (2 \, x\right )} - \log \relax (x)^{2}\right )} e^{\left (-2 \, x\right )}\right ) - 4 \, \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(x)^2+x^4*exp(x)^2*log(x)-6*exp(x)^2*x^4)*log((log(x)^2-x^4*exp(x)^2*log(x)+6*exp(x)^2*x^4)/ex
p(x)^2/x^4)+(-2*x-4)*log(x)^2+2*log(x)-exp(x)^2*x^4)/(x^2*log(x)^2-x^6*exp(x)^2*log(x)+6*x^6*exp(x)^2),x, algo
rithm="giac")

[Out]

(log(-(x^4*e^(2*x)*log(x) - 6*x^4*e^(2*x) - log(x)^2)*e^(-2*x)) - 4*log(x))/x

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maple [C]  time = 0.71, size = 722, normalized size = 21.88

method	result	size
risch	\(-\frac {2 \ln \left ({\mathrm e}^{x}\right )}{x}-\frac {8 \ln \relax (x )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (\frac {i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{x^{4}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{4}}\right )+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{4}\right )^{2}+i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )^{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{x^{4}}\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{2}-i \pi \mathrm {csgn}\left (i {\mathrm e}^{x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )-i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-2 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right )^{2}-2 i \pi +i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-2 x}\right ) \mathrm {csgn}\left (i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right )-2 \ln \left ({\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}-\ln \relax (x )^{2}\right )+i \pi \mathrm {csgn}\left (\frac {i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{x^{4}}\right )^{3}-i \pi \mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right )^{3}-i \pi \mathrm {csgn}\left (i x^{4}\right )^{3}+2 i \pi \mathrm {csgn}\left (\frac {i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{x^{4}}\right )^{2}-i \pi \mathrm {csgn}\left (i x^{3}\right )^{3}-i \pi \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{3}-i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )-i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-2 x} \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-{\mathrm e}^{2 x} \left (\ln \relax (x )-6\right ) x^{4}+\ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{x^{4}}\right ) \mathrm {csgn}\left (\frac {i}{x^{4}}\right )-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2 x}\)	\(722\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-ln(x)^2+x^4*exp(x)^2*ln(x)-6*exp(x)^2*x^4)*ln((ln(x)^2-x^4*exp(x)^2*ln(x)+6*exp(x)^2*x^4)/exp(x)^2/x^4)
+(-2*x-4)*ln(x)^2+2*ln(x)-exp(x)^2*x^4)/(x^2*ln(x)^2-x^6*exp(x)^2*ln(x)+6*x^6*exp(x)^2),x,method=_RETURNVERBOS
E)

[Out]

-2/x*ln(exp(x))-1/2*(-2*I*Pi+8*ln(x)-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2+I*Pi*csgn(I/x
^4*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2)*exp(-2*x))^3-I*Pi*csgn(I*exp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2))^3+2
*I*Pi*csgn(I*exp(x))*csgn(I*exp(2*x))^2-I*Pi*csgn(I*exp(x))^2*csgn(I*exp(2*x))-I*Pi*csgn(I*exp(-2*x))*csgn(I*e
xp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2))^2-I*Pi*csgn(I/x^4*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2)*exp(-2*x))^2*c
sgn(I/x^4)+I*Pi*csgn(I*x)*csgn(I*x^4)^2+I*Pi*csgn(I*x^3)*csgn(I*x^4)^2+I*Pi*csgn(I*x)*csgn(I*x^3)^2+I*Pi*csgn(
I*x^2)*csgn(I*x^3)^2+I*Pi*csgn(I*exp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2))*csgn(I/x^4*(-exp(2*x)*(ln(x)-6)*
x^4+ln(x)^2)*exp(-2*x))^2-I*Pi*csgn(I*x^2)^3-I*Pi*csgn(I*x^4)^3+2*I*Pi*csgn(I/x^4*(-exp(2*x)*(ln(x)-6)*x^4+ln(
x)^2)*exp(-2*x))^2-2*ln(exp(2*x)*(ln(x)-6)*x^4-ln(x)^2)-I*Pi*csgn(I*x^3)^3-I*Pi*csgn(I*x)*csgn(I*x^2)*csgn(I*x
^3)-I*Pi*csgn(I*x)*csgn(I*x^3)*csgn(I*x^4)-I*Pi*csgn(I*exp(2*x))^3+I*Pi*csgn(I*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^
2))*csgn(I*exp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2))^2+I*Pi*csgn(I*exp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)
^2))*csgn(I/x^4*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2)*exp(-2*x))*csgn(I/x^4)+I*Pi*csgn(I*exp(-2*x))*csgn(I*(-exp(2
*x)*(ln(x)-6)*x^4+ln(x)^2))*csgn(I*exp(-2*x)*(-exp(2*x)*(ln(x)-6)*x^4+ln(x)^2)))/x

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maxima [A]  time = 0.41, size = 35, normalized size = 1.06 \begin {gather*} \frac {\log \left (-x^{4} e^{\left (2 \, x\right )} \log \relax (x) + 6 \, x^{4} e^{\left (2 \, x\right )} + \log \relax (x)^{2}\right ) - 4 \, \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(x)^2+x^4*exp(x)^2*log(x)-6*exp(x)^2*x^4)*log((log(x)^2-x^4*exp(x)^2*log(x)+6*exp(x)^2*x^4)/ex
p(x)^2/x^4)+(-2*x-4)*log(x)^2+2*log(x)-exp(x)^2*x^4)/(x^2*log(x)^2-x^6*exp(x)^2*log(x)+6*x^6*exp(x)^2),x, algo
rithm="maxima")

[Out]

(log(-x^4*e^(2*x)*log(x) + 6*x^4*e^(2*x) + log(x)^2) - 4*log(x))/x

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mupad [B]  time = 7.49, size = 32, normalized size = 0.97 \begin {gather*} \frac {\ln \left (\frac {1}{x^4}\right )+\ln \left (6\,x^4-x^4\,\ln \relax (x)+{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^2\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log((exp(-2*x)*(log(x)^2 + 6*x^4*exp(2*x) - x^4*exp(2*x)*log(x)))/x^4)*(log(x)^2 + 6*x^4*exp(2*x) - x^4*
exp(2*x)*log(x)) - 2*log(x) + x^4*exp(2*x) + log(x)^2*(2*x + 4))/(6*x^6*exp(2*x) + x^2*log(x)^2 - x^6*exp(2*x)
*log(x)),x)

[Out]

(log(1/x^4) + log(6*x^4 - x^4*log(x) + exp(-2*x)*log(x)^2))/x

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sympy [A]  time = 1.16, size = 37, normalized size = 1.12 \begin {gather*} \frac {\log {\left (\frac {\left (- x^{4} e^{2 x} \log {\relax (x )} + 6 x^{4} e^{2 x} + \log {\relax (x )}^{2}\right ) e^{- 2 x}}{x^{4}} \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-ln(x)**2+x**4*exp(x)**2*ln(x)-6*exp(x)**2*x**4)*ln((ln(x)**2-x**4*exp(x)**2*ln(x)+6*exp(x)**2*x**
4)/exp(x)**2/x**4)+(-2*x-4)*ln(x)**2+2*ln(x)-exp(x)**2*x**4)/(x**2*ln(x)**2-x**6*exp(x)**2*ln(x)+6*x**6*exp(x)
**2),x)

[Out]

log((-x**4*exp(2*x)*log(x) + 6*x**4*exp(2*x) + log(x)**2)*exp(-2*x)/x**4)/x

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