Optimal. Leaf size=14 \[ 3+\log \left (\log ^2\left (-8+\log \left (e^{2 x}\right )\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps
used = 5, number of rules used = 4, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.267, Rules used = {12, 2437, 2339,
29} \begin {gather*} 2 \log (\log (-2 (4-x))) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2339
Rule 2437
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {1}{(-4+x) \log (-8+2 x)} \, dx\\ &=\text {Subst}\left (\int \frac {2}{x \log (x)} \, dx,x,-8+2 x\right )\\ &=2 \text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,-8+2 x\right )\\ &=2 \text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (2 (-4+x))\right )\\ &=2 \log (\log (-2 (4-x)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 9, normalized size = 0.64 \begin {gather*} 2 \log (\log (2 (-4+x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 10, normalized size = 0.71
method | result | size |
derivativedivides | \(2 \ln \left (\ln \left (2 x -8\right )\right )\) | \(10\) |
default | \(2 \ln \left (\ln \left (2 x -8\right )\right )\) | \(10\) |
norman | \(2 \ln \left (\ln \left (2 x -8\right )\right )\) | \(10\) |
risch | \(2 \ln \left (\ln \left (2 x -8\right )\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.64 \begin {gather*} 2 \, \log \left (\log \left (2 \, x - 8\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 9, normalized size = 0.64 \begin {gather*} 2 \, \log \left (\log \left (2 \, x - 8\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.57 \begin {gather*} 2 \log {\left (\log {\left (2 x - 8 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.64 \begin {gather*} 2 \, \log \left (\log \left (2 \, x - 8\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.84, size = 9, normalized size = 0.64 \begin {gather*} 2\,\ln \left (\ln \left (2\,x-8\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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