Optimal. Leaf size=9 \[ \frac{e^x}{x+1} \]
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Rubi [A] time = 0.0256603, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2197} \[ \frac{e^x}{x+1} \]
Antiderivative was successfully verified.
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Rule 2197
Rubi steps
\begin{align*} \int \frac{e^x x}{(1+x)^2} \, dx &=\frac{e^x}{1+x}\\ \end{align*}
Mathematica [A] time = 0.0229454, size = 9, normalized size = 1. \[ \frac{e^x}{x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 9, normalized size = 1. \begin{align*}{\frac{{{\rm e}^{x}}}{1+x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.942497, size = 11, normalized size = 1.22 \begin{align*} \frac{e^{x}}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74625, size = 18, normalized size = 2. \begin{align*} \frac{e^{x}}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.085104, size = 5, normalized size = 0.56 \begin{align*} \frac{e^{x}}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10392, size = 26, normalized size = 2.89 \begin{align*} \frac{e^{\left (-{\left (x + 1\right )}{\left (\frac{1}{x + 1} - 1\right )}\right )}}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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