Optimal. Leaf size=15 \[ \log \left (\frac {(1-2 x)^2}{e^3 x^8}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {631} \begin {gather*} 2 \log (1-2 x)-8 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {8}{x}+\frac {4}{-1+2 x}\right ) \, dx\\ &=2 \log (1-2 x)-8 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.87 \begin {gather*} 2 \log (1-2 x)-8 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 13, normalized size = 0.87 \begin {gather*} 2 \, \log \left (2 \, x - 1\right ) - 8 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 15, normalized size = 1.00 \begin {gather*} 2 \, \log \left ({\left | 2 \, x - 1 \right |}\right ) - 8 \, \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 = 0.31, size = 14, normalized size = 0.93
method | result | size |
default | \(2 \ln \left (2 x -1\right )-8 \ln \relax (x )\) | \(14\) |
norman | \(2 \ln \left (2 x -1\right )-8 \ln \relax (x )\) | \(14\) |
risch | \(2 \ln \left (2 x -1\right )-8 \ln \relax (x )\) | \(14\) |
meijerg | \(-8 \ln \relax (x )-8 \ln \relax (2)-8 i \pi +2 \ln \left (1-2 x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.87 \begin {gather*} 2 \, \log \left (2 \, x - 1\right ) - 8 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 11, normalized size = 0.73 \begin {gather*} 2\,\ln \left (x-\frac {1}{2}\right )-8\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.80 \begin {gather*} - 8 \log {\relax (x )} + 2 \log {\left (x - \frac {1}{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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