Optimal. Leaf size=31 \[ \frac {e^{x+x^2} x}{-\frac {3}{x}+x \left (x-\log \left (-1+e^4+\log (x)\right )\right )} \]
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Rubi [F] time = 13.28, 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^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{x+x^2} x \left (-6 \left (1-e^4\right )-3 \left (1-e^4\right ) x-7 \left (1-\frac {6 e^4}{7}\right ) x^2-\left (1-e^4\right ) x^3+\left (1-e^4\right ) x^4+2 \left (1-e^4\right ) x^5+\left (-1+e^4\right ) x^3 (1+2 x) \log \left (-1+e^4+\log (x)\right )-\log (x) \left (-6-3 x-6 x^2-x^3+x^4+2 x^5-x^3 (1+2 x) \log \left (-1+e^4+\log (x)\right )\right )\right )}{\left (1-e^4-\log (x)\right ) \left (3-x^3+x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx\\ &=\int \left (\frac {e^{x+x^2} x^2 (1+2 x)}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )}+\frac {e^{x+x^2} x \left (-6 \left (1-e^4\right )-x^2-\left (1-e^4\right ) x^3+6 \log (x)+x^3 \log (x)\right )}{\left (1-e^4-\log (x)\right ) \left (3-x^3+x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}\right ) \, dx\\ &=\int \frac {e^{x+x^2} x^2 (1+2 x)}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )} \, dx+\int \frac {e^{x+x^2} x \left (-6 \left (1-e^4\right )-x^2-\left (1-e^4\right ) x^3+6 \log (x)+x^3 \log (x)\right )}{\left (1-e^4-\log (x)\right ) \left (3-x^3+x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx\\ &=\int \left (-\frac {6 e^{x+x^2} \left (-1+e^4\right ) x}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}+\frac {e^{x+x^2} x^3}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}-\frac {e^{x+x^2} \left (-1+e^4\right ) x^4}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}-\frac {6 e^{x+x^2} x \log (x)}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}-\frac {e^{x+x^2} x^4 \log (x)}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2}\right ) \, dx+\int \left (\frac {e^{x+x^2} x^2}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )}+\frac {2 e^{x+x^2} x^3}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )}\right ) \, dx\\ &=2 \int \frac {e^{x+x^2} x^3}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )} \, dx-6 \int \frac {e^{x+x^2} x \log (x)}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx+\left (1-e^4\right ) \int \frac {e^{x+x^2} x^4}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx+\left (6 \left (1-e^4\right )\right ) \int \frac {e^{x+x^2} x}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx+\int \frac {e^{x+x^2} x^3}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx-\int \frac {e^{x+x^2} x^4 \log (x)}{\left (-1+e^4+\log (x)\right ) \left (-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )\right )^2} \, dx+\int \frac {e^{x+x^2} x^2}{-3+x^3-x^2 \log \left (-1+e^4+\log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 33, normalized size = 1.06 \begin {gather*} -\frac {e^{x+x^2} x^2}{3-x^3+x^2 \log \left (-1+e^4+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 29, normalized size = 0.94 \begin {gather*} \frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \relax (x) - 1\right ) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 5.12, size = 29, normalized size = 0.94 \begin {gather*} \frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \relax (x) - 1\right ) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 30, normalized size = 0.97
method | result | size |
risch | \(\frac {x^{2} {\mathrm e}^{\left (x +1\right ) x}}{x^{3}-x^{2} \ln \left (\ln \relax (x )+{\mathrm e}^{4}-1\right )-3}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 29, normalized size = 0.94 \begin {gather*} \frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \relax (x) - 1\right ) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.96, size = 268, normalized size = 8.65 \begin {gather*} -\frac {x^3\,\left (6\,{\mathrm {e}}^{x^2+x}-12\,{\mathrm {e}}^{x^2+x+4}+6\,{\mathrm {e}}^{x^2+x+8}-12\,{\mathrm {e}}^{x^2+x}\,\ln \relax (x)+12\,{\mathrm {e}}^{x^2+x+4}\,\ln \relax (x)+6\,{\mathrm {e}}^{x^2+x}\,{\ln \relax (x)}^2\right )-x^5\,\left ({\mathrm {e}}^{x^2+x+4}-{\mathrm {e}}^{x^2+x}+{\mathrm {e}}^{x^2+x}\,\ln \relax (x)\right )+x^6\,\left ({\mathrm {e}}^{x^2+x}-2\,{\mathrm {e}}^{x^2+x+4}+{\mathrm {e}}^{x^2+x+8}-2\,{\mathrm {e}}^{x^2+x}\,\ln \relax (x)+2\,{\mathrm {e}}^{x^2+x+4}\,\ln \relax (x)+{\mathrm {e}}^{x^2+x}\,{\ln \relax (x)}^2\right )}{\left (x^2\,\ln \left ({\mathrm {e}}^4+\ln \relax (x)-1\right )-x^3+3\right )\,\left (6\,x+6\,x\,{\ln \relax (x)}^2-x^3\,\ln \relax (x)-2\,x^4\,\ln \relax (x)-12\,x\,{\mathrm {e}}^4+6\,x\,{\mathrm {e}}^8+x^4\,{\ln \relax (x)}^2-x^3\,{\mathrm {e}}^4-2\,x^4\,{\mathrm {e}}^4+x^4\,{\mathrm {e}}^8-12\,x\,\ln \relax (x)+x^3+x^4+12\,x\,{\mathrm {e}}^4\,\ln \relax (x)+2\,x^4\,{\mathrm {e}}^4\,\ln \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.75, size = 27, normalized size = 0.87 \begin {gather*} \frac {x^{2} e^{x^{2} + x}}{x^{3} - x^{2} \log {\left (\log {\relax (x )} - 1 + e^{4} \right )} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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