Optimal. Leaf size=11 \[ \log \left (\frac {4 x}{12-x}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 615} \begin {gather*} \log (x)-\log (12-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 615
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (12 \int \frac {1}{-12 x+x^2} \, dx\right )\\ &=-\log (12-x)+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.73 \begin {gather*} -12 \left (\frac {1}{12} \log (12-x)-\frac {\log (x)}{12}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 9, normalized size = 0.82 \begin {gather*} -\log \left (x - 12\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 = 11, normalized size = 1.00 \begin {gather*} -\log \left ({\left | x - 12 \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 = 0.22, size = 10, normalized size = 0.91
method | result | size |
default | \(\ln \relax (x )-\ln \left (x -12\right )\) | \(10\) |
norman | \(\ln \relax (x )-\ln \left (x -12\right )\) | \(10\) |
risch | \(\ln \relax (x )-\ln \left (x -12\right )\) | \(10\) |
meijerg | \(\ln \relax (x )-2 \ln \relax (2)-\ln \relax (3)+i \pi -\ln \left (1-\frac {x}{12}\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 9, normalized size = 0.82 \begin {gather*} -\log \left (x - 12\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.89, size = 8, normalized size = 0.73 \begin {gather*} 2\,\mathrm {atanh}\left (\frac {x}{6}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.64 \begin {gather*} \log {\relax (x )} - \log {\left (x - 12 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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