3.72.16 \(\int \frac {e^{\frac {e^{2/x} x-x \log (3 x^4-6 x^2 \log (6)+3 \log ^2(6))}{\log (3 x^4-6 x^2 \log (6)+3 \log ^2(6))}} (4 e^{2/x} x^3+e^{2/x} (2 x^2-x^3+(-2+x) \log (6)) \log (3 x^4-6 x^2 \log (6)+3 \log ^2(6))+(x^3-x \log (6)) \log ^2(3 x^4-6 x^2 \log (6)+3 \log ^2(6)))}{(-x^3+x \log (6)) \log ^2(3 x^4-6 x^2 \log (6)+3 \log ^2(6))} \, dx\)

Optimal. Leaf size=31 \[ -5+e^{x \left (-1+\frac {e^{2/x}}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}\right )} \]

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Rubi [F]  time = 93.11, 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 {\exp \left (\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((E^(2/x)*x - x*Log[3*x^4 - 6*x^2*Log[6] + 3*Log[6]^2])/Log[3*x^4 - 6*x^2*Log[6] + 3*Log[6]^2])*(4*E^(2
/x)*x^3 + E^(2/x)*(2*x^2 - x^3 + (-2 + x)*Log[6])*Log[3*x^4 - 6*x^2*Log[6] + 3*Log[6]^2] + (x^3 - x*Log[6])*Lo
g[3*x^4 - 6*x^2*Log[6] + 3*Log[6]^2]^2))/((-x^3 + x*Log[6])*Log[3*x^4 - 6*x^2*Log[6] + 3*Log[6]^2]^2),x]

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{x \left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\\ &=\int \frac {e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 e^{2/x} x^3+e^{2/x} (-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )+\left (-x^3+x \log (6)\right ) \log ^2\left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\\ &=\int \left (-e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx\\ &=-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\\ &=-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3+(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\\ &=-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \left (\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log (6) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3+2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )-x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )-2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )+x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log (6) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx\\ &=\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3+2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )-x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )-2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )+x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx\\ &=\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3-(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3+(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx\\ &=\frac {\int \left (\frac {4 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}-\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \log (6)}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}-\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \log (6)}{x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx}{\log (6)}+\frac {\int \left (\frac {4 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \log (6)}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^3}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2 \log (6)}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx\\ &=-\left (2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}}{x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\right )+2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx-\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^3}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {4 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {4 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 29, normalized size = 0.94 \begin {gather*} e^{x \left (-1+\frac {e^{2/x}}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^(x*(-1 + E^(2/x)/Log[3*(x^2 - Log[6])^2]))

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fricas [A]  time = 0.61, size = 56, normalized size = 1.81 \begin {gather*} e^{\left (\frac {x e^{\frac {2}{x}} - x \log \left (3 \, x^{4} - 6 \, x^{2} \log \relax (6) + 3 \, \log \relax (6)^{2}\right )}{\log \left (3 \, x^{4} - 6 \, x^{2} \log \relax (6) + 3 \, \log \relax (6)^{2}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^((x*e^(2/x) - x*log(3*x^4 - 6*x^2*log(6) + 3*log(6)^2))/log(3*x^4 - 6*x^2*log(6) + 3*log(6)^2))

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giac [A]  time = 8.35, size = 35, normalized size = 1.13 \begin {gather*} e^{\left (-x + \frac {x e^{\frac {2}{x}}}{\log \left (3 \, x^{4} - 6 \, x^{2} \log \relax (6) + 3 \, \log \relax (6)^{2}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(-x + x*e^(2/x)/log(3*x^4 - 6*x^2*log(6) + 3*log(6)^2))

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maple [C]  time = 1.29, size = 219, normalized size = 7.06

method	result	size
risch	\({\mathrm e}^{-\frac {x \left (-i \pi \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right )^{3}+2 i \pi \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )\right )-i \pi \,\mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right ) \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )\right )^{2}+2 \ln \relax (3)-2 \,{\mathrm e}^{\frac {2}{x}}+4 \ln \left (-x^{2}+\ln \relax (2)+\ln \relax (3)\right )\right )}{-i \pi \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right )^{3}+2 i \pi \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )\right )-i \pi \,\mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )^{2}\right ) \mathrm {csgn}\left (i \left (-x^{2}+\ln \relax (6)\right )\right )^{2}+2 \ln \relax (3)+4 \ln \left (-x^{2}+\ln \relax (2)+\ln \relax (3)\right )}}\)	\(219\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(-x*(-I*Pi*csgn(I*(-x^2+ln(6))^2)^3+2*I*Pi*csgn(I*(-x^2+ln(6))^2)^2*csgn(I*(-x^2+ln(6)))-I*Pi*csgn(I*(-x^2+
ln(6))^2)*csgn(I*(-x^2+ln(6)))^2+2*ln(3)-2*exp(2/x)+4*ln(-x^2+ln(2)+ln(3)))/(-I*Pi*csgn(I*(-x^2+ln(6))^2)^3+2*
I*Pi*csgn(I*(-x^2+ln(6))^2)^2*csgn(I*(-x^2+ln(6)))-I*Pi*csgn(I*(-x^2+ln(6))^2)*csgn(I*(-x^2+ln(6)))^2+2*ln(3)+
4*ln(-x^2+ln(2)+ln(3))))

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [B]  time = 4.59, size = 36, normalized size = 1.16 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{2/x}}{\ln \left (3\,x^4-6\,\ln \relax (6)\,x^2+3\,{\ln \relax (6)}^2\right )}}\,{\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp((x*exp(2/x))/log(3*log(6)^2 - 6*x^2*log(6) + 3*x^4))*exp(-x)

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sympy [B]  time = 1.40, size = 53, normalized size = 1.71 \begin {gather*} e^{\frac {x e^{\frac {2}{x}} - x \log {\left (3 x^{4} - 6 x^{2} \log {\relax (6 )} + 3 \log {\relax (6 )}^{2} \right )}}{\log {\left (3 x^{4} - 6 x^{2} \log {\relax (6 )} + 3 \log {\relax (6 )}^{2} \right )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp((x*exp(2/x) - x*log(3*x**4 - 6*x**2*log(6) + 3*log(6)**2))/log(3*x**4 - 6*x**2*log(6) + 3*log(6)**2))

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