Optimal. Leaf size=33 \[ e^{1+\left (5-e^x\right ) \left (-3-x+\frac {-e^{-1+x}+\log \left (x^2\right )}{x}\right )} \]
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Rubi [F] time = 32.52, 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 {-5 e^{-1+x}-14 x-5 x^2+e^x \left (e^{-1+x}+3 x+x^2\right )+\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (10+e^{-1+x} (5-5 x)-5 x^2+e^x \left (-2+4 x^2+x^3+e^{-1+x} (-1+2 x)\right )+\left (-5+e^x (1-x)\right ) \log \left (x^2\right )\right )}{x^2} \, 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 (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (10+e^{-1+x} (5-5 x)-5 x^2+e^x \left (-2+4 x^2+x^3+e^{-1+x} (-1+2 x)\right )+\left (-5+e^x (1-x)\right ) \log \left (x^2\right )\right )}{x^2} \, dx\\ &=\int \left (\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+2 x)}{x^2}-\frac {5 \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2+\log \left (x^2\right )\right )}{x^2}+\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5 \left (1-\frac {2 e}{5}\right )-5 x+4 e x^2+e x^3+e \log \left (x^2\right )-e x \log \left (x^2\right )\right )}{x^2}\right ) \, dx\\ &=-\left (5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2+\log \left (x^2\right )\right )}{x^2} \, dx\right )+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+2 x)}{x^2} \, dx+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5 \left (1-\frac {2 e}{5}\right )-5 x+4 e x^2+e x^3+e \log \left (x^2\right )-e x \log \left (x^2\right )\right )}{x^2} \, dx\\ &=-\left (5 \int \left (\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2\right )}{x^2}+\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2}\right ) \, dx\right )+\int \left (-\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}+\frac {2 \exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x}\right ) \, dx+\int \left (\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5-2 e-5 x+4 e x^2+e x^3\right )}{x^2}-\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+x) \log \left (x^2\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2\right )}{x^2} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5-2 e-5 x+4 e x^2+e x^3\right )}{x^2} \, dx-\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+x) \log \left (x^2\right )}{x^2} \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \left (\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )-\frac {2 \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}\right ) \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \left (4 \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )+\frac {(5-2 e) \exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}-\frac {5 \exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x}+\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) x\right ) \, dx-\int \left (-\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2}+\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x}\right ) \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx+4 \int \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \, dx-5 \int \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \, dx-5 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx+10 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+(5-2 e) \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) x \, dx+\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.23, size = 51, normalized size = 1.55 \begin {gather*} e^{-14-\frac {5 e^{-1+x}}{x}+\frac {e^{-1+2 x}}{x}-5 x+e^x (3+x)} \left (x^2\right )^{\frac {5-e^x}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.07, size = 60, normalized size = 1.82 \begin {gather*} e^{\left (-\frac {{\left ({\left (5 \, x^{2} + 14 \, x\right )} e - {\left ({\left (x^{2} + 3 \, x\right )} e - 5\right )} e^{x} - {\left (5 \, e - e^{\left (x + 1\right )}\right )} \log \left (x^{2}\right ) - e^{\left (2 \, x\right )}\right )} e^{\left (-1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.04, size = 53, normalized size = 1.61 \begin {gather*} e^{\left (x e^{x} - 5 \, x - \frac {e^{x} \log \left (x^{2}\right )}{x} + \frac {e^{\left (2 \, x - 1\right )}}{x} - \frac {5 \, e^{\left (x - 1\right )}}{x} + \frac {5 \, \log \left (x^{2}\right )}{x} + 3 \, e^{x} - 14\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.76, size = 156, normalized size = 4.73
method | result | size |
risch | \({\mathrm e}^{-\frac {-i {\mathrm e}^{x} \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i {\mathrm e}^{x} \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i {\mathrm e}^{x} \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+5 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-10 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+5 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \,{\mathrm e}^{x} x^{2}+4 \,{\mathrm e}^{x} \ln \relax (x )-2 \,{\mathrm e}^{2 x -1}-6 \,{\mathrm e}^{x} x +10 x^{2}-20 \ln \relax (x )+10 \,{\mathrm e}^{x -1}+28 x}{2 x}}\) | \(156\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.77, size = 49, normalized size = 1.48 \begin {gather*} e^{\left (x e^{x} - 5 \, x - \frac {2 \, e^{x} \log \relax (x)}{x} + \frac {e^{\left (2 \, x - 1\right )}}{x} - \frac {5 \, e^{\left (x - 1\right )}}{x} + \frac {10 \, \log \relax (x)}{x} + 3 \, e^{x} - 14\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.76, size = 50, normalized size = 1.52 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-1}}{x}}\,{\mathrm {e}}^{-14}\,{\mathrm {e}}^{3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {5\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^x}{x}}\,{\left (\frac {1}{x^2}\right )}^{\frac {{\mathrm {e}}^x-5}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.90, size = 46, normalized size = 1.39 \begin {gather*} e^{\frac {- 5 x^{2} - 14 x + \left (5 - e^{x}\right ) \log {\left (x^{2} \right )} + \left (x^{2} + 3 x + \frac {e^{x}}{e}\right ) e^{x} - \frac {5 e^{x}}{e}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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