Optimal. Leaf size=15 \[ \frac{x^2}{2}-x+\log (x+1) \]
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Rubi [A] time = 0.00575, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{x^2}{2}-x+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x^2}{1+x} \, dx &=\int \left (-1+x+\frac{1}{1+x}\right ) \, dx\\ &=-x+\frac{x^2}{2}+\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0030243, size = 19, normalized size = 1.27 \[ \frac{1}{2} (x+1)^2-2 (x+1)+\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \begin{align*} -x+{\frac{{x}^{2}}{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 = 0.950728, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, x^{2} - x + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.80622, size = 35, normalized size = 2.33 \begin{align*} \frac{1}{2} \, x^{2} - x + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067622, size = 10, normalized size = 0.67 \begin{align*} \frac{x^{2}}{2} - x + \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04549, size = 19, normalized size = 1.27 \begin{align*} \frac{1}{2} \, x^{2} - x + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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