Optimal. Leaf size=28 \[ 3 \left (\frac {e^{-e^x+e^{x-x^2}-5 x}}{x}+x\right ) \]
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Rubi [F] time = 3.60, 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 {3 x+\frac {e^{-e^x+e^{x-x^2}-5 x} \left (-3-15 x-3 e^x x+e^{x-x^2} \left (3 x-6 x^2\right )\right )}{x}}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3 e^{-e^x+e^{x-x^2}-x (4+x)} (-1+2 x)}{x}+\frac {3 e^{-e^x-5 x} \left (-e^{e^{x-x^2}}-5 e^{e^{x-x^2}} x-e^{e^{x-x^2}+x} x+e^{e^x+5 x} x^2\right )}{x^2}\right ) \, dx\\ &=-\left (3 \int \frac {e^{-e^x+e^{x-x^2}-x (4+x)} (-1+2 x)}{x} \, dx\right )+3 \int \frac {e^{-e^x-5 x} \left (-e^{e^{x-x^2}}-5 e^{e^{x-x^2}} x-e^{e^{x-x^2}+x} x+e^{e^x+5 x} x^2\right )}{x^2} \, dx\\ &=3 \int \left (1+\frac {e^{-e^x+e^{(1-x) x}-5 x} (-1-5 x)}{x^2}-\frac {e^{-e^x+e^{x-x^2}-4 x}}{x}\right ) \, dx-3 \int \left (2 e^{-e^x+e^{x-x^2}-x (4+x)}-\frac {e^{-e^x+e^{x-x^2}-x (4+x)}}{x}\right ) \, dx\\ &=3 x+3 \int \frac {e^{-e^x+e^{(1-x) x}-5 x} (-1-5 x)}{x^2} \, dx-3 \int \frac {e^{-e^x+e^{x-x^2}-4 x}}{x} \, dx+3 \int \frac {e^{-e^x+e^{x-x^2}-x (4+x)}}{x} \, dx-6 \int e^{-e^x+e^{x-x^2}-x (4+x)} \, dx\\ &=3 x+3 \int \left (-\frac {e^{-e^x+e^{(1-x) x}-5 x}}{x^2}-\frac {5 e^{-e^x+e^{(1-x) x}-5 x}}{x}\right ) \, dx-3 \int \frac {e^{-e^x+e^{x-x^2}-4 x}}{x} \, dx+3 \int \frac {e^{-e^x+e^{x-x^2}-x (4+x)}}{x} \, dx-6 \int e^{-e^x+e^{x-x^2}-x (4+x)} \, dx\\ &=3 x-3 \int \frac {e^{-e^x+e^{(1-x) x}-5 x}}{x^2} \, dx-3 \int \frac {e^{-e^x+e^{x-x^2}-4 x}}{x} \, dx+3 \int \frac {e^{-e^x+e^{x-x^2}-x (4+x)}}{x} \, dx-6 \int e^{-e^x+e^{x-x^2}-x (4+x)} \, dx-15 \int \frac {e^{-e^x+e^{(1-x) x}-5 x}}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.89, size = 29, normalized size = 1.04 \begin {gather*} \frac {3 e^{-e^x+e^{x-x^2}-5 x}}{x}+3 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 27, normalized size = 0.96 \begin {gather*} 3 \, x + 3 \, e^{\left (-5 \, x + e^{\left (-x^{2} + x\right )} - e^{x} - \log \relax (x)\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 {3 \, {\left ({\left ({\left (2 \, x^{2} - x\right )} e^{\left (-x^{2} + x\right )} + x e^{x} + 5 \, x + 1\right )} e^{\left (-5 \, x + e^{\left (-x^{2} + x\right )} - e^{x} - \log \relax (x)\right )} - x\right )}}{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 = 26, normalized size = 0.93
method | result | size |
risch | \(3 x +\frac {3 \,{\mathrm e}^{-{\mathrm e}^{x}+{\mathrm e}^{-x \left (x -1\right )}-5 x}}{x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 26, normalized size = 0.93 \begin {gather*} 3 \, x + \frac {3 \, e^{\left (-5 \, x + e^{\left (-x^{2} + x\right )} - e^{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.64, size = 28, normalized size = 1.00 \begin {gather*} 3\,x+\frac {3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-{\mathrm {e}}^x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 20, normalized size = 0.71 \begin {gather*} 3 x + \frac {3 e^{- 5 x - e^{x} + e^{- x^{2} + x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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