Optimal. Leaf size=26 \[ e^{\frac {\left (-7+e^{\left (-6+e^2-x^2\right )^2}\right ) x}{16+\log (x)}} \]
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Rubi [F] time = 68.24, 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 {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(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 {\exp \left (\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=\int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} \left (-105+e^{\left (6-e^2+x^2\right )^2} \left (15-64 \left (-6+e^2\right ) x^2+64 x^4\right )+\left (-7+e^{\left (6-e^2+x^2\right )^2} \left (1-4 \left (-6+e^2\right ) x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=\int \left (-\frac {7 e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2}\right ) \, dx\\ &=-\left (7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2} \, dx\right )+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=-\left (7 \int \left (-\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2}+\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)}\right ) \, dx\right )+\int \left (-\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)}\right ) \, dx\\ &=7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)} \, dx\\ &=7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \left (\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)}-\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (-6+e^2\right ) x^2}{16+\log (x)}+\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)}\right ) \, dx\\ &=4 \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)} \, dx+7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx+\left (4 \left (6-e^2\right )\right ) \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^2}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 15.48, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.68, size = 36, normalized size = 1.38 \begin {gather*} e^{\left (\frac {x e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} - 7 \, x}{\log \relax (x) + 16}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.78, size = 43, normalized size = 1.65 \begin {gather*} e^{\left (\frac {x e^{\left (x^{4} - 2 \, x^{2} e^{2} + 12 \, x^{2} + e^{4} - 12 \, e^{2} + 36\right )}}{\log \relax (x) + 16} - \frac {7 \, x}{\log \relax (x) + 16}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 36, normalized size = 1.38
method | result | size |
risch | \({\mathrm e}^{\frac {x \left ({\mathrm e}^{x^{4}-2 x^{2} {\mathrm e}^{2}+12 x^{2}-12 \,{\mathrm e}^{2}+{\mathrm e}^{4}+36}-7\right )}{16+\ln \relax (x )}}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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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.
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mupad [B] time = 3.95, size = 48, normalized size = 1.85 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-12\,{\mathrm {e}}^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{36}\,{\mathrm {e}}^{12\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}}{\ln \relax (x)+16}}\,{\mathrm {e}}^{-\frac {7\,x}{\ln \relax (x)+16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.16, size = 37, normalized size = 1.42 \begin {gather*} e^{\frac {x e^{x^{4} + 12 x^{2} + \left (- 2 x^{2} - 12\right ) e^{2} + 36 + e^{4}} - 7 x}{\log {\relax (x )} + 16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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