Optimal. Leaf size=23 \[ -e^{-5+x} x+2^{-1/x} e^{-2+x} x \]
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Rubi [F] time = 0.53, 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 {2^{-1/x} \left (2^{\frac {1}{x}} e^{-5+x} \left (-x-x^2\right )+e^{-2+x} \left (x+x^2+\log (2)\right )\right )}{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 (-e^{-5+x}+2^{-1/x} e^{-2+x}-e^{-5+x} x+2^{-1/x} e^{-2+x} x+\frac {2^{-1/x} e^{-2+x} \log (2)}{x}\right ) \, dx\\ &=\log (2) \int \frac {2^{-1/x} e^{-2+x}}{x} \, dx-\int e^{-5+x} \, dx+\int 2^{-1/x} e^{-2+x} \, dx-\int e^{-5+x} x \, dx+\int 2^{-1/x} e^{-2+x} x \, dx\\ &=-e^{-5+x}-e^{-5+x} x+\log (2) \int \frac {2^{-1/x} e^{-2+x}}{x} \, dx+\int e^{-5+x} \, dx+\int 2^{-1/x} e^{-2+x} \, dx+\int 2^{-1/x} e^{-2+x} x \, dx\\ &=-e^{-5+x} x+\log (2) \int \frac {2^{-1/x} e^{-2+x}}{x} \, dx+\int 2^{-1/x} e^{-2+x} \, dx+\int 2^{-1/x} e^{-2+x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.42, size = 20, normalized size = 0.87 \begin {gather*} e^{-5+x} \left (-1+2^{-1/x} e^3\right ) x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 30, normalized size = 1.30 \begin {gather*} -\frac {{\left (2^{\left (\frac {1}{x}\right )} x e^{\left (x - 2\right )} - x e^{\left (x + 1\right )}\right )} e^{\left (-3\right )}}{2^{\left (\frac {1}{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^{2} + x\right )} 2^{\left (\frac {1}{x}\right )} e^{\left (x - 5\right )} - {\left (x^{2} + x + \log \relax (2)\right )} e^{\left (x - 2\right )}}{2^{\left (\frac {1}{x}\right )} x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 22, normalized size = 0.96
method | result | size |
risch | \(-x \,{\mathrm e}^{x -5}+2^{-\frac {1}{x}} x \,{\mathrm e}^{x -2}\) | \(22\) |
norman | \(\left (x \,{\mathrm e}^{3} {\mathrm e}^{x -5}-{\mathrm e}^{x -5} {\mathrm e}^{\frac {\ln \relax (2)}{x}} x \right ) {\mathrm e}^{-\frac {\ln \relax (2)}{x}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 29, normalized size = 1.26 \begin {gather*} x e^{\left (x - \frac {\log \relax (2)}{x} - 2\right )} - {\left (x - 1\right )} e^{\left (x - 5\right )} - e^{\left (x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.24, size = 19, normalized size = 0.83 \begin {gather*} -x\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^{-5}-\frac {{\mathrm {e}}^{-2}}{2^{1/x}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 10.64, size = 17, normalized size = 0.74 \begin {gather*} \left (- x + x e^{3} e^{- \frac {\log {\relax (2 )}}{x}}\right ) e^{x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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