Optimal. Leaf size=36 \[ -x+\frac {5 x}{-x+\frac {2+e^{6-x-x^2} x}{\log \left (x^2\right )}} \]
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Rubi [F] time = 15.55, 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 {16+6 e^{6-x-x^2} x-e^{12-2 x-2 x^2} x^2+\left (10+4 x+e^{6-x-x^2} \left (7 x^2+10 x^3\right )\right ) \log \left (x^2\right )-x^2 \log ^2\left (x^2\right )}{4+4 e^{6-x-x^2} x+e^{12-2 x-2 x^2} x^2+\left (-4 x-2 e^{6-x-x^2} x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 x (1+x)} \left (16+6 e^{6-x-x^2} x-e^{12-2 x-2 x^2} x^2+\left (10+4 x+e^{6-x-x^2} \left (7 x^2+10 x^3\right )\right ) \log \left (x^2\right )-x^2 \log ^2\left (x^2\right )\right )}{\left (2 e^{x+x^2}+e^6 x-e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx\\ &=\int \left (-1+\frac {5 e^{-6-x-x^2+2 x (1+x)} \left (2+x \log \left (x^2\right )+2 x^2 \log \left (x^2\right )\right )}{x}+\frac {5 e^{2 x (1+x)} \log \left (x^2\right ) \left (2-4 x^2+x^2 \log \left (x^2\right )+2 x^3 \log \left (x^2\right )\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2}+\frac {5 e^{-6+2 x (1+x)} \left (-4-4 x^2 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )+2 x^3 \log ^2\left (x^2\right )\right )}{x \left (2 e^{x+x^2}+e^6 x-e^{x+x^2} x \log \left (x^2\right )\right )}\right ) \, dx\\ &=-x+5 \int \frac {e^{-6-x-x^2+2 x (1+x)} \left (2+x \log \left (x^2\right )+2 x^2 \log \left (x^2\right )\right )}{x} \, dx+5 \int \frac {e^{2 x (1+x)} \log \left (x^2\right ) \left (2-4 x^2+x^2 \log \left (x^2\right )+2 x^3 \log \left (x^2\right )\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{-6+2 x (1+x)} \left (-4-4 x^2 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )+2 x^3 \log ^2\left (x^2\right )\right )}{x \left (2 e^{x+x^2}+e^6 x-e^{x+x^2} x \log \left (x^2\right )\right )} \, dx\\ &=-x-\frac {5 e^{-6-x-x^2+2 x (1+x)} \left (x \log \left (x^2\right )+2 x^2 \log \left (x^2\right )\right )}{x (1-2 (1+x))}+5 \int \frac {e^{-6+2 x+2 x^2} \left (-4-4 x^2 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )+2 x^3 \log ^2\left (x^2\right )\right )}{x \left (2 e^{x+x^2}+e^6 x-e^{x+x^2} x \log \left (x^2\right )\right )} \, dx+5 \int \left (\frac {2 e^{2 x (1+x)} \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2}-\frac {4 e^{2 x (1+x)} x^2 \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2}+\frac {e^{2 x (1+x)} x^2 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2}+\frac {2 e^{2 x (1+x)} x^3 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2}\right ) \, dx\\ &=-x-\frac {5 e^{-6-x-x^2+2 x (1+x)} \left (x \log \left (x^2\right )+2 x^2 \log \left (x^2\right )\right )}{x (1-2 (1+x))}+5 \int \frac {e^{2 x (1+x)} x^2 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx+5 \int \left (\frac {4 e^{-6+2 x+2 x^2}}{x \left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )}+\frac {4 e^{-6+2 x+2 x^2} x \log \left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )}-\frac {e^{-6+2 x+2 x^2} x \log ^2\left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )}-\frac {2 e^{-6+2 x+2 x^2} x^2 \log ^2\left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )}\right ) \, dx+10 \int \frac {e^{2 x (1+x)} \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx+10 \int \frac {e^{2 x (1+x)} x^3 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{2 x (1+x)} x^2 \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx\\ &=-x-\frac {5 e^{-6-x-x^2+2 x (1+x)} \left (x \log \left (x^2\right )+2 x^2 \log \left (x^2\right )\right )}{x (1-2 (1+x))}+5 \int \frac {e^{2 x (1+x)} x^2 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx-5 \int \frac {e^{-6+2 x+2 x^2} x \log ^2\left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )} \, dx+10 \int \frac {e^{2 x (1+x)} \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx+10 \int \frac {e^{2 x (1+x)} x^3 \log ^2\left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx-10 \int \frac {e^{-6+2 x+2 x^2} x^2 \log ^2\left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )} \, dx-20 \int \frac {e^{2 x (1+x)} x^2 \log \left (x^2\right )}{\left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )^2} \, dx+20 \int \frac {e^{-6+2 x+2 x^2}}{x \left (-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )\right )} \, dx+20 \int \frac {e^{-6+2 x+2 x^2} x \log \left (x^2\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.23, size = 52, normalized size = 1.44 \begin {gather*} -x-\frac {5 \left (2 e^{x+x^2}+e^6 x\right )}{-2 e^{x+x^2}-e^6 x+e^{x+x^2} x \log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 58, normalized size = 1.61 \begin {gather*} \frac {x^{2} \log \left (x^{2}\right ) - {\left (x^{2} - 5 \, x\right )} e^{\left (-x^{2} - x + 6\right )} - 2 \, x + 10}{x e^{\left (-x^{2} - x + 6\right )} - x \log \left (x^{2}\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 61, normalized size = 1.69 \begin {gather*} -\frac {x^{2} e^{\left (-x^{2} - x + 6\right )} - x^{2} \log \left (x^{2}\right ) - 5 \, x \log \left (x^{2}\right ) + 2 \, x}{x e^{\left (-x^{2} - x + 6\right )} - x \log \left (x^{2}\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 69, normalized size = 1.92
method | result | size |
norman | \(\frac {x^{2} \ln \left (x^{2}\right )+5 x \,{\mathrm e}^{-x^{2}-x +6}-2 x -x^{2} {\mathrm e}^{-x^{2}-x +6}+10}{x \,{\mathrm e}^{-x^{2}-x +6}-x \ln \left (x^{2}\right )+2}\) | \(69\) |
default | \(\frac {x^{2} \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right )+\left (5 \ln \left (x^{2}\right )-10 \ln \relax (x )-2\right ) x +10 x \ln \relax (x )-x^{2} {\mathrm e}^{-x^{2}-x +6}+2 x^{2} \ln \relax (x )}{x \,{\mathrm e}^{-x^{2}-x +6}-2 x \ln \relax (x )-x \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right )+2}\) | \(92\) |
risch | \(-x +\frac {20+10 x \,{\mathrm e}^{-\left (3+x \right ) \left (x -2\right )}}{i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}+2 x \,{\mathrm e}^{-\left (3+x \right ) \left (x -2\right )}-4 x \ln \relax (x )+4}\) | \(93\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 54, normalized size = 1.50 \begin {gather*} -\frac {x^{2} e^{6} - 5 \, x e^{6} - 2 \, {\left (x^{2} \log \relax (x) - x + 5\right )} e^{\left (x^{2} + x\right )}}{x e^{6} - 2 \, {\left (x \log \relax (x) - 1\right )} e^{\left (x^{2} + x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.68, size = 68, normalized size = 1.89 \begin {gather*} -\frac {x\,\left (x+2\,{\mathrm {e}}^{x^2+x-6}-5\,\ln \left (x^2\right )\,{\mathrm {e}}^{x^2+x-6}-x\,\ln \left (x^2\right )\,{\mathrm {e}}^{x^2+x-6}\right )}{x+2\,{\mathrm {e}}^{x^2+x-6}-x\,\ln \left (x^2\right )\,{\mathrm {e}}^{x^2+x-6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 27, normalized size = 0.75 \begin {gather*} - x + \frac {5 x \log {\left (x^{2} \right )}}{x e^{- x^{2} - x + 6} - x \log {\left (x^{2} \right )} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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