Optimal. Leaf size=29 \[ -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (4+x) \]
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Rubi [A]
time = 0.03, 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 = {1626}
\begin {gather*} -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 1626
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 \begin {gather*} -\frac {11}{14} \log (3-x)+\frac {3}{2} \log (5-x)+\frac {2}{7} \log (4+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 20, normalized size = 0.69
method | result | size |
default | \(\frac {2 \ln \left (x +4\right )}{7}-\frac {11 \ln \left (x -3\right )}{14}+\frac {3 \ln \left (-5+x \right )}{2}\) | \(20\) |
norman | \(\frac {2 \ln \left (x +4\right )}{7}-\frac {11 \ln \left (x -3\right )}{14}+\frac {3 \ln \left (-5+x \right )}{2}\) | \(20\) |
risch | \(\frac {2 \ln \left (x +4\right )}{7}-\frac {11 \ln \left (x -3\right )}{14}+\frac {3 \ln \left (-5+x \right )}{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.66 \begin {gather*} \frac {2}{7} \, \log \left (x + 4\right ) - \frac {11}{14} \, \log \left (x - 3\right ) + \frac {3}{2} \, \log \left (x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 0.66 \begin {gather*} \frac {2}{7} \, \log \left (x + 4\right ) - \frac {11}{14} \, \log \left (x - 3\right ) + \frac {3}{2} \, \log \left (x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 0.83 \begin {gather*} \frac {3 \log {\left (x - 5 \right )}}{2} - \frac {11 \log {\left (x - 3 \right )}}{14} + \frac {2 \log {\left (x + 4 \right )}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.24, size = 22, normalized size = 0.76 \begin {gather*} \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 ) \end {gather*}
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 \begin {gather*} \frac {2\,\ln \left (x+4\right )}{7}-\frac {11\,\ln \left (x-3\right )}{14}+\frac {3\,\ln \left (x-5\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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