Optimal. Leaf size=28 \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (x+2) \]
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Rubi [A] time = 0.0100071, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {88} \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{x^2}{(-3+x) (2+x)^2} \, dx &=\int \left (\frac{9}{25 (-3+x)}-\frac{4}{5 (2+x)^2}+\frac{16}{25 (2+x)}\right ) \, dx\\ &=\frac{4}{5 (2+x)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0158948, size = 26, normalized size = 0.93 \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (x-3)+\frac{16}{25} \log (x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 21, normalized size = 0.8 \begin{align*}{\frac{4}{10+5\,x}}+{\frac{16\,\ln \left ( 2+x \right ) }{25}}+{\frac{9\,\ln \left ( -3+x \right ) }{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926318, size = 27, normalized size = 0.96 \begin{align*} \frac{4}{5 \,{\left (x + 2\right )}} + \frac{16}{25} \, \log \left (x + 2\right ) + \frac{9}{25} \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83164, size = 89, normalized size = 3.18 \begin{align*} \frac{16 \,{\left (x + 2\right )} \log \left (x + 2\right ) + 9 \,{\left (x + 2\right )} \log \left (x - 3\right ) + 20}{25 \,{\left (x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.113319, size = 22, normalized size = 0.79 \begin{align*} \frac{9 \log{\left (x - 3 \right )}}{25} + \frac{16 \log{\left (x + 2 \right )}}{25} + \frac{4}{5 x + 10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04837, size = 35, normalized size = 1.25 \begin{align*} \frac{4}{5 \,{\left (x + 2\right )}} + \log \left ({\left | x + 2 \right |}\right ) + \frac{9}{25} \, \log \left ({\left | -\frac{5}{x + 2} + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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