Optimal. Leaf size=17 \[ \frac{x^2}{2}-2 x+6 \log (x+2) \]
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Rubi [A] time = 0.0082738, antiderivative size = 17, 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 = {697} \[ \frac{x^2}{2}-2 x+6 \log (x+2) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin{align*} \int \frac{2+x^2}{2+x} \, dx &=\int \left (-2+x+\frac{6}{2+x}\right ) \, dx\\ &=-2 x+\frac{x^2}{2}+6 \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0034374, size = 18, normalized size = 1.06 \[ \frac{x^2}{2}-2 x+6 \log (x+2)-6 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \begin{align*} -2\,x+{\frac{{x}^{2}}{2}}+6\,\ln \left ( 2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.968912, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{2} \, x^{2} - 2 \, x + 6 \, \log \left (x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.964359, size = 41, normalized size = 2.41 \begin{align*} \frac{1}{2} \, x^{2} - 2 \, x + 6 \, \log \left (x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070396, size = 14, normalized size = 0.82 \begin{align*} \frac{x^{2}}{2} - 2 x + 6 \log{\left (x + 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13121, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{2} \, x^{2} - 2 \, x + 6 \, \log \left ({\left | x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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