Optimal. Leaf size=18 \[ \log \left (e^{25} (-5+x) \log \left (4-\frac {36}{x}+\log (x)\right )\right ) \]
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Rubi [A] time = 1.28, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {6741, 6742, 6684} \begin {gather*} \log (5-x)+\log \left (\log \left (-\frac {36}{x}+\log (x)+4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-180+31 x+x^2+\left (-36 x+4 x^2+x^2 \log (x)\right ) \log \left (\frac {-36+4 x+x \log (x)}{x}\right )}{(5-x) x (36-4 x-x \log (x)) \log \left (4-\frac {36}{x}+\log (x)\right )} \, dx\\ &=\int \left (\frac {1}{-5+x}+\frac {36+x}{x (-36+4 x+x \log (x)) \log \left (4-\frac {36}{x}+\log (x)\right )}\right ) \, dx\\ &=\log (5-x)+\int \frac {36+x}{x (-36+4 x+x \log (x)) \log \left (4-\frac {36}{x}+\log (x)\right )} \, dx\\ &=\log (5-x)+\log \left (\log \left (4-\frac {36}{x}+\log (x)\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 18, normalized size = 1.00 \begin {gather*} \log (5-x)+\log \left (\log \left (4-\frac {36}{x}+\log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 20, normalized size = 1.11 \begin {gather*} \log \left (x - 5\right ) + \log \left (\log \left (\frac {x \log \relax (x) + 4 \, x - 36}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 21, normalized size = 1.17 \begin {gather*} \log \left (x - 5\right ) + \log \left (-\log \left (x \log \relax (x) + 4 \, x - 36\right ) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 21, normalized size = 1.17
method | result | size |
default | \(\ln \left (x -5\right )+\ln \left (\ln \left (\frac {x \ln \relax (x )+4 x -36}{x}\right )\right )\) | \(21\) |
risch | \(\ln \left (x -5\right )+\ln \left (\ln \left (-36+\left (\ln \relax (x )+4\right ) x \right )+\frac {i \left (\pi \,\mathrm {csgn}\left (i \left (-36+\left (\ln \relax (x )+4\right ) x \right )\right ) \mathrm {csgn}\left (\frac {i \left (-36+\left (\ln \relax (x )+4\right ) x \right )}{x}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (-36+\left (\ln \relax (x )+4\right ) x \right )\right ) \mathrm {csgn}\left (\frac {i \left (-36+\left (\ln \relax (x )+4\right ) x \right )}{x}\right ) \mathrm {csgn}\left (\frac {i}{x}\right )-\pi \mathrm {csgn}\left (\frac {i \left (-36+\left (\ln \relax (x )+4\right ) x \right )}{x}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i \left (-36+\left (\ln \relax (x )+4\right ) x \right )}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )+2 i \ln \relax (x )\right )}{2}\right )\) | \(140\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 21, normalized size = 1.17 \begin {gather*} \log \left (x - 5\right ) + \log \left (\log \left (x \log \relax (x) + 4 \, x - 36\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.27, size = 20, normalized size = 1.11 \begin {gather*} \ln \left (\ln \left (\frac {4\,x+x\,\ln \relax (x)-36}{x}\right )\right )+\ln \left (x-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 19, normalized size = 1.06 \begin {gather*} \log {\left (x - 5 \right )} + \log {\left (\log {\left (\frac {x \log {\relax (x )} + 4 x - 36}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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