Optimal. Leaf size=17 \[ 5 \log (2-x)-6 \log (x)+\log (x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {801} \[ 5 \log (2-x)-6 \log (x)+\log (x+2) \]
Antiderivative was successfully verified.
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Rule 801
Rubi steps
\begin {align*} \int \frac {24+8 x}{x \left (-4+x^2\right )} \, dx &=\int \left (\frac {5}{-2+x}-\frac {6}{x}+\frac {1}{2+x}\right ) \, dx\\ &=5 \log (2-x)-6 \log (x)+\log (2+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 1.59 \[ 8 \left (\frac {5}{8} \log (2-x)-\frac {3 \log (x)}{4}+\frac {1}{8} \log (x+2)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 15, normalized size = 0.88 \[ \log \left (x + 2\right ) + 5 \, \log \left (x - 2\right ) - 6 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 18, normalized size = 1.06 \[ \log \left ({\left | x + 2 \right |}\right ) + 5 \, \log \left ({\left | x - 2 \right |}\right ) - 6 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 16, normalized size = 0.94 \[ -6 \ln \relax (x )+5 \ln \left (x -2\right )+\ln \left (x +2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 15, normalized size = 0.88 \[ \log \left (x + 2\right ) + 5 \, \log \left (x - 2\right ) - 6 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 15, normalized size = 0.88 \[ 5\,\ln \left (x-2\right )+\ln \left (x+2\right )-6\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.88 \[ - 6 \log {\relax (x )} + 5 \log {\left (x - 2 \right )} + \log {\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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