Optimal. Leaf size=16 \[ \frac{e^{a x}}{a^2 (a x+1)} \]
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Rubi [A] time = 0.0315516, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2197} \[ \frac{e^{a x}}{a^2 (a x+1)} \]
Antiderivative was successfully verified.
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Rule 2197
Rubi steps
\begin{align*} \int \frac{e^{a x} x}{(1+a x)^2} \, dx &=\frac{e^{a x}}{a^2 (1+a x)}\\ \end{align*}
Mathematica [A] time = 0.045405, size = 16, normalized size = 1. \[ \frac{e^{a x}}{a^2 (a x+1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 1. \begin{align*}{\frac{{{\rm e}^{ax}}}{{a}^{2} \left ( ax+1 \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.950543, size = 22, normalized size = 1.38 \begin{align*} \frac{e^{\left (a x\right )}}{a^{3} x + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55689, size = 31, normalized size = 1.94 \begin{align*} \frac{e^{\left (a x\right )}}{a^{3} x + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116405, size = 12, normalized size = 0.75 \begin{align*} \frac{e^{a x}}{a^{3} x + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10811, size = 38, normalized size = 2.38 \begin{align*} \frac{e^{\left (-{\left (a x + 1\right )}{\left (\frac{1}{a x + 1} - 1\right )}\right )}}{{\left (a x + 1\right )} a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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