Optimal. Leaf size=22 \[ -25+e^{\frac {5-x+e^{-x} x^2}{x}} \]
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Rubi [F] time = 1.13, 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+\frac {e^{-x} \left (e^x (5-x)+x^2\right )}{x}} \left (-5 e^x+x^2-x^3\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 {e^{-1+\frac {5}{x}+\left (-1+e^{-x}\right ) x} \left (-5 e^x+x^2-x^3\right )}{x^2} \, dx\\ &=\int \left (e^{-1+\frac {5}{x}+\left (-1+e^{-x}\right ) x}-\frac {5 e^{-1+\frac {5}{x}+x+\left (-1+e^{-x}\right ) x}}{x^2}-e^{-1+\frac {5}{x}+\left (-1+e^{-x}\right ) x} x\right ) \, dx\\ &=-\left (5 \int \frac {e^{-1+\frac {5}{x}+x+\left (-1+e^{-x}\right ) x}}{x^2} \, dx\right )+\int e^{-1+\frac {5}{x}+\left (-1+e^{-x}\right ) x} \, dx-\int e^{-1+\frac {5}{x}+\left (-1+e^{-x}\right ) x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 16, normalized size = 0.73 \begin {gather*} e^{-1+\frac {5}{x}+e^{-x} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 25, normalized size = 1.14 \begin {gather*} e^{\left (x + \frac {{\left (x^{2} - {\left (x^{2} + x - 5\right )} e^{x}\right )} e^{\left (-x\right )}}{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 {{\left (x^{3} - x^{2} + 5 \, e^{x}\right )} e^{\left (-x + \frac {{\left (x^{2} - {\left (x - 5\right )} e^{x}\right )} e^{\left (-x\right )}}{x}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 22, normalized size = 1.00
method | result | size |
norman | \({\mathrm e}^{\frac {\left (\left (5-x \right ) {\mathrm e}^{x}+x^{2}\right ) {\mathrm e}^{-x}}{x}}\) | \(22\) |
risch | \({\mathrm e}^{-\frac {\left ({\mathrm e}^{x} x -x^{2}-5 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}{x}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 14, normalized size = 0.64 \begin {gather*} e^{\left (x e^{\left (-x\right )} + \frac {5}{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.31, size = 16, normalized size = 0.73 \begin {gather*} {\mathrm {e}}^{-1}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{5/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 15, normalized size = 0.68 \begin {gather*} e^{\frac {\left (x^{2} + \left (5 - x\right ) e^{x}\right ) e^{- x}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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