Optimal. Leaf size=16 \[ 4 \log \left ((-x+x (-4+2 x))^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.75, number of steps
used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {642}
\begin {gather*} 8 \log \left (5 x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=8 \log \left (5 x-2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.69 \begin {gather*} 8 (\log (5-2 x)+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.74, size = 11, normalized size = 0.69
method | result | size |
default | \(8 \ln \left (x \left (2 x -5\right )\right )\) | \(11\) |
risch | \(8 \ln \left (2 x^{2}-5 x \right )\) | \(13\) |
norman | \(8 \ln \left (x \right )+8 \ln \left (2 x -5\right )\) | \(14\) |
meijerg | \(8 \ln \left (-\frac {2 x}{5}+1\right )+8 \ln \left (x \right )+8 \ln \left (2\right )-8 \ln \left (5\right )+8 i \pi \) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 12, normalized size = 0.75 \begin {gather*} 8 \, \log \left (2 \, x^{2} - 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 12, normalized size = 0.75 \begin {gather*} 8 \, \log \left (2 \, x^{2} - 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.62 \begin {gather*} 8 \log {\left (2 x^{2} - 5 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 13, normalized size = 0.81 \begin {gather*} 8 \, \log \left ({\left | 2 \, x^{2} - 5 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 10, normalized size = 0.62 \begin {gather*} 8\,\ln \left (x\,\left (2\,x-5\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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