Optimal. Leaf size=11 \[ \frac{e^{-x} x}{\log (x)} \]
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Rubi [A] time = 0.0245364, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {2201} \[ \frac{e^{-x} x}{\log (x)} \]
Antiderivative was successfully verified.
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Rule 2201
Rubi steps
\begin{align*} \int \frac{e^{-x} (-1+(1-x) \log (x))}{\log ^2(x)} \, dx &=\frac{e^{-x} x}{\log (x)}\\ \end{align*}
Mathematica [A] time = 0.0078425, size = 11, normalized size = 1. \[ \frac{e^{-x} x}{\log (x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.013, size = 11, normalized size = 1. \begin{align*}{\frac{x}{{{\rm e}^{x}}\ln \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08985, size = 14, normalized size = 1.27 \begin{align*} \frac{x e^{\left (-x\right )}}{\log \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57698, size = 23, normalized size = 2.09 \begin{align*} \frac{x e^{\left (-x\right )}}{\log \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.283352, size = 7, normalized size = 0.64 \begin{align*} \frac{x e^{- x}}{\log{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07873, size = 14, normalized size = 1.27 \begin{align*} \frac{x e^{\left (-x\right )}}{\log \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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