Optimal. Leaf size=26 \[ e^{2-\frac {1}{20} e^{-1+x^2} (1-2 x)+x}-3 \log (x) \]
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Rubi [F] time = 1.38, 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 {-30+e^{\frac {1}{20} \left (40+e^{-1+x^2} (-1+2 x)\right )} \left (10 e^x x+e^{-1+x+x^2} \left (x-x^2+2 x^3\right )\right )}{10 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \frac {-30+e^{\frac {1}{20} \left (40+e^{-1+x^2} (-1+2 x)\right )} \left (10 e^x x+e^{-1+x+x^2} \left (x-x^2+2 x^3\right )\right )}{x} \, dx\\ &=\frac {1}{10} \int \left (-\frac {30}{x}+e^{1+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \left (10 e+e^{x^2}-e^{x^2} x+2 e^{x^2} x^2\right )\right ) \, dx\\ &=-3 \log (x)+\frac {1}{10} \int e^{1+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \left (10 e+e^{x^2}-e^{x^2} x+2 e^{x^2} x^2\right ) \, dx\\ &=-3 \log (x)+\frac {1}{10} \int e^{1+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \left (10 e+e^{x^2} \left (1-x+2 x^2\right )\right ) \, dx\\ &=-3 \log (x)+\frac {1}{10} \int \left (10 e^{2+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)}+e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \left (1-x+2 x^2\right )\right ) \, dx\\ &=-3 \log (x)+\frac {1}{10} \int e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \left (1-x+2 x^2\right ) \, dx+\int e^{2+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \, dx\\ &=-3 \log (x)+\frac {1}{10} \int \left (e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)}-e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} x+2 e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} x^2\right ) \, dx+\int e^{2+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \, dx\\ &=-3 \log (x)+\frac {1}{10} \int e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \, dx-\frac {1}{10} \int e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} x \, dx+\frac {1}{5} \int e^{1+x+x^2+\frac {1}{20} e^{-1+x^2} (-1+2 x)} x^2 \, dx+\int e^{2+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.37, size = 26, normalized size = 1.00 \begin {gather*} e^{2+x+\frac {1}{20} e^{-1+x^2} (-1+2 x)}-3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 43, normalized size = 1.65 \begin {gather*} -{\left (3 \, e^{\left (x^{2} - 1\right )} \log \relax (x) - e^{\left (x^{2} + \frac {1}{20} \, {\left (2 \, x - 1\right )} e^{\left (x^{2} - 1\right )} + x + 1\right )}\right )} e^{\left (-x^{2} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left ({\left (2 \, x^{3} - x^{2} + x\right )} e^{\left (x^{2} + x - 1\right )} + 10 \, x e^{x}\right )} e^{\left (\frac {1}{20} \, {\left (2 \, x - 1\right )} e^{\left (x^{2} - 1\right )} + 2\right )} - 30}{10 \, x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 31, normalized size = 1.19
method | result | size |
risch | \(-3 \ln \relax (x )+{\mathrm e}^{x +\frac {{\mathrm e}^{\left (x -1\right ) \left (x +1\right )} x}{10}-\frac {{\mathrm e}^{\left (x -1\right ) \left (x +1\right )}}{20}+2}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 26, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{10} \, x e^{\left (x^{2} - 1\right )} + x - \frac {1}{20} \, e^{\left (x^{2} - 1\right )} + 2\right )} - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.12, size = 26, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{x-\frac {{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-1}}{20}+\frac {x\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-1}}{10}+2}-3\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 48.25, size = 24, normalized size = 0.92 \begin {gather*} e^{x} e^{\left (\frac {x}{10} - \frac {1}{20}\right ) e^{x^{2} - 1} + 2} - 3 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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