Optimal. Leaf size=14 \[ 2 \log (x+1)-\frac{1}{x+1} \]
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Rubi [A] time = 0.0053683, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ 2 \log (x+1)-\frac{1}{x+1} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+2 x}{(1+x)^2} \, dx &=\int \left (\frac{1}{(1+x)^2}+\frac{2}{1+x}\right ) \, dx\\ &=-\frac{1}{1+x}+2 \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0036457, size = 14, normalized size = 1. \[ 2 \log (x+1)-\frac{1}{x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 15, normalized size = 1.1 \begin{align*} - \left ( 1+x \right ) ^{-1}+2\,\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.930263, size = 19, normalized size = 1.36 \begin{align*} -\frac{1}{x + 1} + 2 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87043, size = 49, normalized size = 3.5 \begin{align*} \frac{2 \,{\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 = 0.075777, size = 10, normalized size = 0.71 \begin{align*} 2 \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 = 1.04253, size = 20, normalized size = 1.43 \begin{align*} -\frac{1}{x + 1} + 2 \, \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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