Optimal. Leaf size=10 \[ \frac{1}{x+1}+\log (x+1) \]
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Rubi [A] time = 0.0043905, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {43} \[ \frac{1}{x+1}+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x}{(1+x)^2} \, dx &=\int \left (-\frac{1}{(1+x)^2}+\frac{1}{1+x}\right ) \, dx\\ &=\frac{1}{1+x}+\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0027193, size = 10, normalized size = 1. \[ \frac{1}{x+1}+\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 11, normalized size = 1.1 \begin{align*} \left ( 1+x \right ) ^{-1}+\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.927928, size = 14, normalized size = 1.4 \begin{align*} \frac{1}{x + 1} + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63569, size = 46, normalized size = 4.6 \begin{align*} \frac{{\left (x + 1\right )} \log \left (x + 1\right ) + 1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074338, size = 8, normalized size = 0.8 \begin{align*} \log{\left (x + 1 \right )} + \frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0972, size = 15, normalized size = 1.5 \begin{align*} \frac{1}{x + 1} + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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