Optimal. Leaf size=22 \[ \log ^2(\log (5)) \log ^2(4-x+5 \log (\log (4)) \log (\log (25))) \]
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Rubi [A]
time = 0.03, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2437, 2338}
\begin {gather*} \log ^2(\log (5)) \log ^2(-x+4+5 \log (\log (4)) \log (\log (25))) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2338
Rule 2437
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 \log ^2(\log (5))\right ) \int \frac {\log (4-x+5 \log (\log (4)) \log (\log (25)))}{4-x+5 \log (\log (4)) \log (\log (25))} \, dx\right )\\ &=\left (2 \log ^2(\log (5))\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,4-x+5 \log (\log (4)) \log (\log (25))\right )\\ &=\log ^2(\log (5)) \log ^2(4-x+5 \log (\log (4)) \log (\log (25)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} \log ^2(\log (5)) \log ^2(4-x+5 \log (\log (4)) \log (\log (25))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 27, normalized size = 1.23
method | result | size |
derivativedivides | \(\ln \left (5 \ln \left (2 \ln \left (2\right )\right ) \ln \left (2 \ln \left (5\right )\right )-x +4\right )^{2} \ln \left (\ln \left (5\right )\right )^{2}\) | \(27\) |
default | \(\ln \left (5 \ln \left (2 \ln \left (2\right )\right ) \ln \left (2 \ln \left (5\right )\right )-x +4\right )^{2} \ln \left (\ln \left (5\right )\right )^{2}\) | \(27\) |
norman | \(\ln \left (5 \ln \left (2 \ln \left (2\right )\right ) \ln \left (2 \ln \left (5\right )\right )-x +4\right )^{2} \ln \left (\ln \left (5\right )\right )^{2}\) | \(27\) |
risch | \(\ln \left (\ln \left (5\right )\right )^{2} \ln \left (5 \left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )\right ) \left (\ln \left (2\right )+\ln \left (\ln \left (5\right )\right )\right )-x +4\right )^{2}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 26, normalized size = 1.18 \begin {gather*} \log \left (5 \, \log \left (2 \, \log \left (5\right )\right ) \log \left (2 \, \log \left (2\right )\right ) - x + 4\right )^{2} \log \left (\log \left (5\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 33, normalized size = 1.50 \begin {gather*} \log \left (5 \, \log \left (2\right ) \log \left (2 \, \log \left (2\right )\right ) + 5 \, \log \left (2 \, \log \left (2\right )\right ) \log \left (\log \left (5\right )\right ) - x + 4\right )^{2} \log \left (\log \left (5\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 27, normalized size = 1.23 \begin {gather*} \log {\left (- x + 5 \log {\left (2 \log {\left (2 \right )} \right )} \log {\left (2 \log {\left (5 \right )} \right )} + 4 \right )}^{2} \log {\left (\log {\left (5 \right )} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 26, normalized size = 1.18 \begin {gather*} \log \left (5 \, \log \left (2 \, \log \left (5\right )\right ) \log \left (2 \, \log \left (2\right )\right ) - x + 4\right )^{2} \log \left (\log \left (5\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.93, size = 23, normalized size = 1.05 \begin {gather*} {\ln \left (\ln \left ({\ln \left (4\right )}^5\right )\,\ln \left (\ln \left (25\right )\right )-x+4\right )}^2\,{\ln \left (\ln \left (5\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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