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 = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.40, size = 27, normalized size = 0.96 \[ \frac {16 \, {\left (x + 2\right )} \log \left (x + 2\right ) + 9 \, {\left (x + 2\right )} \log \left (x - 3\right ) + 20}{25 \, {\left (x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 26, normalized size = 0.93 \[ \frac {4}{5 \, {\left (x + 2\right )}} + \log \left ({\left | x + 2 \right |}\right ) + \frac {9}{25} \, \log \left ({\left | -\frac {5}{x + 2} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 21, normalized size = 0.75 \[ \frac {9 \ln \left (x -3\right )}{25}+\frac {16 \ln \left (x +2\right )}{25}+\frac {4}{5 \left (x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 20, normalized size = 0.71 \[ \frac {4}{5 \, {\left (x + 2\right )}} + \frac {16}{25} \, \log \left (x + 2\right ) + \frac {9}{25} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 22, normalized size = 0.79 \[ \frac {16\,\ln \left (x+2\right )}{25}+\frac {9\,\ln \left (x-3\right )}{25}+\frac {4}{5\,\left (x+2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.79 \[ \frac {9 \log {\left (x - 3 \right )}}{25} + \frac {16 \log {\left (x + 2 \right )}}{25} + \frac {4}{5 x + 10} \]
Verification of antiderivative is not currently implemented for this CAS.
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