Optimal. Leaf size=16 \[ \log \left (\frac {\frac {12}{x}+x}{(25-x)^4}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 19, normalized size of antiderivative = 1.19, number of steps used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2074, 260} \begin {gather*} \log \left (x^2+12\right )-4 \log (25-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 260
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4}{-25+x}-\frac {1}{x}+\frac {2 x}{12+x^2}\right ) \, dx\\ &=-4 \log (25-x)-\log (x)+2 \int \frac {x}{12+x^2} \, dx\\ &=-4 \log (25-x)-\log (x)+\log \left (12+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.19 \begin {gather*} -4 \log (25-x)-\log (x)+\log \left (12+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 17, normalized size = 1.06 \begin {gather*} \log \left (x^{2} + 12\right ) - 4 \, \log \left (x - 25\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 19, normalized size = 1.19 \begin {gather*} \log \left (x^{2} + 12\right ) - 4 \, \log \left ({\left | x - 25 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 18, normalized size = 1.12
method | result | size |
default | \(-\ln \relax (x )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
norman | \(-\ln \relax (x )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
risch | \(-\ln \relax (x )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 17, normalized size = 1.06 \begin {gather*} \log \left (x^{2} + 12\right ) - 4 \, \log \left (x - 25\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 17, normalized size = 1.06 \begin {gather*} \ln \left (x^2+12\right )-4\,\ln \left (x-25\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.94 \begin {gather*} - \log {\relax (x )} - 4 \log {\left (x - 25 \right )} + \log {\left (x^{2} + 12 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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