Optimal. Leaf size=16 \[ \frac {e^{a x}}{a^2 (a x+1)} \]
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Rubi [A] time = 0.03, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.05, size = 16, normalized size = 1.00 \[ \frac {e^{a x}}{a^2 (a x+1)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 16, normalized size = 1.00 \[ \frac {e^{\left (a x\right )}}{a^{3} x + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.19, size = 45, normalized size = 2.81 \[ -\frac {e^{\left (-{\left (a x + 1\right )} {\left (\frac {1}{a x + 1} - 1\right )}\right )}}{{\left (a x + 1\right )} a^{2} {\left (\frac {1}{a x + 1} - 1\right )} - a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {{\mathrm e}^{a x}}{\left (a x +1\right ) a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 16, normalized size = 1.00 \[ \frac {e^{\left (a x\right )}}{a^{3} x + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 15, normalized size = 0.94 \[ \frac {{\mathrm {e}}^{a\,x}}{a^2\,\left (a\,x+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.75 \[ \frac {e^{a x}}{a^{3} x + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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