Optimal. Leaf size=25 \[ e^{\frac {144 \left (8+e^x\right )}{5 \left (-x+\frac {x^2}{\log ^2(x)}\right )^2}} \]
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Rubi [F] time = 29.51, 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 {\left (1152+144 e^x\right ) \log ^4(x)}{5 x^4-10 x^3 \log ^2(x)+5 x^2 \log ^4(x)}\right ) \left (\left (-4608 x-576 e^x x\right ) \log ^3(x)+\left (4608 x+e^x \left (576 x-144 x^2\right )\right ) \log ^4(x)+\left (-2304+e^x (-288+144 x)\right ) \log ^6(x)\right )}{-5 x^6+15 x^5 \log ^2(x)-15 x^4 \log ^4(x)+5 x^3 \log ^6(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {144 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x) \left (4 \left (8+e^x\right ) x+\left (-32+e^x (-4+x)\right ) x \log (x)+\left (16-e^x (-2+x)\right ) \log ^3(x)\right )}{5 x^3 \left (x-\log ^2(x)\right )^3} \, dx\\ &=\frac {144}{5} \int \frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x) \left (4 \left (8+e^x\right ) x+\left (-32+e^x (-4+x)\right ) x \log (x)+\left (16-e^x (-2+x)\right ) \log ^3(x)\right )}{x^3 \left (x-\log ^2(x)\right )^3} \, dx\\ &=\frac {144}{5} \int \left (\frac {32 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x)}{x^2 \left (x-\log ^2(x)\right )^3}-\frac {32 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^4(x)}{x^2 \left (x-\log ^2(x)\right )^3}+\frac {16 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^6(x)}{x^3 \left (x-\log ^2(x)\right )^3}+\frac {\exp \left (x+\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x) \left (4 x-4 x \log (x)+x^2 \log (x)+2 \log ^3(x)-x \log ^3(x)\right )}{x^3 \left (x-\log ^2(x)\right )^3}\right ) \, dx\\ &=\frac {144}{5} \int \frac {\exp \left (x+\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x) \left (4 x-4 x \log (x)+x^2 \log (x)+2 \log ^3(x)-x \log ^3(x)\right )}{x^3 \left (x-\log ^2(x)\right )^3} \, dx+\frac {2304}{5} \int \frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^6(x)}{x^3 \left (x-\log ^2(x)\right )^3} \, dx+\frac {4608}{5} \int \frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x)}{x^2 \left (x-\log ^2(x)\right )^3} \, dx-\frac {4608}{5} \int \frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^4(x)}{x^2 \left (x-\log ^2(x)\right )^3} \, dx\\ &=\frac {144}{5} \int \frac {\exp \left (x+\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log ^3(x) \left (4 x+(-4+x) x \log (x)-(-2+x) \log ^3(x)\right )}{x^3 \left (x-\log ^2(x)\right )^3} \, dx+\frac {2304}{5} \int \left (-\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{x^3}+\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{\left (x-\log ^2(x)\right )^3}-\frac {3 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{x \left (x-\log ^2(x)\right )^2}+\frac {3 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{x^2 \left (x-\log ^2(x)\right )}\right ) \, dx+\frac {4608}{5} \int \left (\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log (x)}{x \left (x-\log ^2(x)\right )^3}-\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right ) \log (x)}{x^2 \left (x-\log ^2(x)\right )^2}\right ) \, dx-\frac {4608}{5} \int \left (\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{\left (x-\log ^2(x)\right )^3}-\frac {2 \exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{x \left (x-\log ^2(x)\right )^2}+\frac {\exp \left (\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}\right )}{x^2 \left (x-\log ^2(x)\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 28, normalized size = 1.12 \begin {gather*} e^{\frac {144 \left (8+e^x\right ) \log ^4(x)}{5 x^2 \left (x-\log ^2(x)\right )^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 34, normalized size = 1.36 \begin {gather*} e^{\left (\frac {144 \, {\left (e^{x} + 8\right )} \log \relax (x)^{4}}{5 \, {\left (x^{2} \log \relax (x)^{4} - 2 \, x^{3} \log \relax (x)^{2} + x^{4}\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.37, size = 62, normalized size = 2.48 \begin {gather*} e^{\left (\frac {144 \, e^{x} \log \relax (x)^{4}}{5 \, {\left (x^{2} \log \relax (x)^{4} - 2 \, x^{3} \log \relax (x)^{2} + x^{4}\right )}} + \frac {1152 \, \log \relax (x)^{4}}{5 \, {\left (x^{2} \log \relax (x)^{4} - 2 \, x^{3} \log \relax (x)^{2} + x^{4}\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 25, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{\frac {144 \left ({\mathrm e}^{x}+8\right ) \ln \relax (x )^{4}}{5 x^{2} \left (\ln \relax (x )^{2}-x \right )^{2}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 4.07, size = 108, normalized size = 4.32 \begin {gather*} e^{\left (\frac {288 \, e^{x}}{5 \, {\left (\log \relax (x)^{4} - x \log \relax (x)^{2}\right )}} + \frac {144 \, e^{x}}{5 \, {\left (\log \relax (x)^{4} - 2 \, x \log \relax (x)^{2} + x^{2}\right )}} + \frac {2304}{5 \, {\left (\log \relax (x)^{4} - x \log \relax (x)^{2}\right )}} + \frac {1152}{5 \, {\left (\log \relax (x)^{4} - 2 \, x \log \relax (x)^{2} + x^{2}\right )}} + \frac {144 \, e^{x}}{5 \, x^{2}} + \frac {1152}{5 \, x^{2}} + \frac {288 \, e^{x}}{5 \, x \log \relax (x)^{2}} + \frac {2304}{5 \, x \log \relax (x)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.10, size = 43, normalized size = 1.72 \begin {gather*} {\mathrm {e}}^{\frac {1152\,{\ln \relax (x)}^4+144\,{\mathrm {e}}^x\,{\ln \relax (x)}^4}{5\,x^4-10\,x^3\,{\ln \relax (x)}^2+5\,x^2\,{\ln \relax (x)}^4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.51, size = 37, normalized size = 1.48 \begin {gather*} e^{\frac {\left (144 e^{x} + 1152\right ) \log {\relax (x )}^{4}}{5 x^{4} - 10 x^{3} \log {\relax (x )}^{2} + 5 x^{2} \log {\relax (x )}^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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