Optimal. Leaf size=12 \[ \log (\log (4 (-5+\log (5-20 x)))) \]
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Rubi [A]
time = 0.04, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12, 6816}
\begin {gather*} \log (\log (4 \log (5-20 x)-20)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {1}{(5-20 x+(-1+4 x) \log (5-20 x)) \log (-20+4 \log (5-20 x))} \, dx\\ &=\log (\log (-20+4 \log (5-20 x)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 12, normalized size = 1.00 \begin {gather*} \log (\log (4 (-5+\log (5-20 x)))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 284.06, size = 13, normalized size = 1.08
method | result | size |
norman | \(\ln \left (\ln \left (4 \ln \left (-20 x +5\right )-20\right )\right )\) | \(13\) |
risch | \(\ln \left (\ln \left (4 \ln \left (-20 x +5\right )-20\right )\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains complex when optimal does not.
time = 0.52, size = 20, normalized size = 1.67 \begin {gather*} \log \left (2 \, \log \left (2\right ) + \log \left (i \, \pi + \log \left (5\right ) + \log \left (4 \, x - 1\right ) - 5\right )\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 = 1.00 \begin {gather*} \log \left (\log \left (4 \, \log \left (-20 \, x + 5\right ) - 20\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 12, normalized size = 1.00 \begin {gather*} \log {\left (\log {\left (4 \log {\left (5 - 20 x \right )} - 20 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 12, normalized size = 1.00 \begin {gather*} \log \left (\log \left (4 \, \log \left (-20 \, x + 5\right ) - 20\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.04, size = 12, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (4\,\ln \left (5-20\,x\right )-20\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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