Optimal. Leaf size=29 \[ -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (x+4) \]
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Rubi [A] time = 0.05, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1612} \[ -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (x+4) \]
Antiderivative was successfully verified.
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Rule 1612
Rubi steps
\begin {align*} \int \frac {2+x^2}{(-5+x) (-3+x) (4+x)} \, dx &=\int \left (\frac {3}{2 (-5+x)}-\frac {11}{14 (-3+x)}+\frac {2}{7 (4+x)}\right ) \, dx\\ &=-\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (4+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \[ -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (x+4) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 19, normalized size = 0.66 \[ \frac {2}{7} \, \log \left (x + 4\right ) - \frac {11}{14} \, \log \left (x - 3\right ) + \frac {3}{2} \, \log \left (x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 22, normalized size = 0.76 \[ \frac {2}{7} \, \log \left ({\left | x + 4 \right |}\right ) - \frac {11}{14} \, \log \left ({\left | x - 3 \right |}\right ) + \frac {3}{2} \, \log \left ({\left | x - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 20, normalized size = 0.69 \[ \frac {3 \ln \left (x -5\right )}{2}-\frac {11 \ln \left (x -3\right )}{14}+\frac {2 \ln \left (x +4\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.17, size = 19, normalized size = 0.66 \[ \frac {2}{7} \, \log \left (x + 4\right ) - \frac {11}{14} \, \log \left (x - 3\right ) + \frac {3}{2} \, \log \left (x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.18, size = 19, normalized size = 0.66 \[ \frac {2\,\ln \left (x+4\right )}{7}-\frac {11\,\ln \left (x-3\right )}{14}+\frac {3\,\ln \left (x-5\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 24, normalized size = 0.83 \[ \frac {3 \log {\left (x - 5 \right )}}{2} - \frac {11 \log {\left (x - 3 \right )}}{14} + \frac {2 \log {\left (x + 4 \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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