Optimal. Leaf size=25 \[ \log \left (-5 x+\frac {\log \left (5 x+\log \left (\frac {6-x}{x}\right )\right )}{\log (x)}\right ) \]
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Rubi [A]
time = 10.83, antiderivative size = 28, normalized size of antiderivative = 1.12, number of steps
used = 6, number of rules used = 5, integrand size = 180, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6820, 6874,
2339, 29, 6816} \begin {gather*} \log \left (5 x \log (x)-\log \left (5 x+\log \left (\frac {6}{x}-1\right )\right )\right )-\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 6816
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\left (\left (-6+30 x-5 x^2\right ) \log (x)\right )-5 (-6+x) x \left (5 x+\log \left (-1+\frac {6}{x}\right )\right ) \log ^2(x)-(-6+x) \left (5 x+\log \left (-1+\frac {6}{x}\right )\right ) \log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )}{(6-x) x \left (5 x+\log \left (-1+\frac {6}{x}\right )\right ) \log (x) \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right )} \, dx\\ &=\int \left (-\frac {1}{x \log (x)}+\frac {-6+30 x-155 x^2+25 x^3-30 x \log \left (-1+\frac {6}{x}\right )+5 x^2 \log \left (-1+\frac {6}{x}\right )-150 x^2 \log (x)+25 x^3 \log (x)-30 x \log \left (-1+\frac {6}{x}\right ) \log (x)+5 x^2 \log \left (-1+\frac {6}{x}\right ) \log (x)}{(-6+x) x \left (5 x+\log \left (-1+\frac {6}{x}\right )\right ) \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right )}\right ) \, dx\\ &=-\int \frac {1}{x \log (x)} \, dx+\int \frac {-6+30 x-155 x^2+25 x^3-30 x \log \left (-1+\frac {6}{x}\right )+5 x^2 \log \left (-1+\frac {6}{x}\right )-150 x^2 \log (x)+25 x^3 \log (x)-30 x \log \left (-1+\frac {6}{x}\right ) \log (x)+5 x^2 \log \left (-1+\frac {6}{x}\right ) \log (x)}{(-6+x) x \left (5 x+\log \left (-1+\frac {6}{x}\right )\right ) \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right )} \, dx\\ &=\log \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right )-\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-\log (\log (x))+\log \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 28, normalized size = 1.12 \begin {gather*} -\log (\log (x))+\log \left (5 x \log (x)-\log \left (5 x+\log \left (-1+\frac {6}{x}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.66, size = 113, normalized size = 4.52
method | result | size |
default | \(-\ln \left (\ln \left (x \right )\right )+\ln \left (-5 x \ln \left (x \right )+\ln \left (i \pi -\ln \left (x \right )+\ln \left (x -6\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )+\mathrm {csgn}\left (i \left (x -6\right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )^{2} \left (\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )-1\right )+5 x \right )\right )\) | \(113\) |
risch | \(-\ln \left (\ln \left (x \right )\right )+\ln \left (-5 x \ln \left (x \right )+\ln \left (i \pi -\ln \left (x \right )+\ln \left (x -6\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )+\mathrm {csgn}\left (i \left (x -6\right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )^{2} \left (\mathrm {csgn}\left (\frac {i \left (x -6\right )}{x}\right )-1\right )+5 x \right )\right )\) | \(113\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 28, normalized size = 1.12 \begin {gather*} \log \left (-5 \, x \log \left (x\right ) + \log \left (5 \, x - \log \left (x\right ) + \log \left (-x + 6\right )\right )\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 27, normalized size = 1.08 \begin {gather*} \log \left (-5 \, x \log \left (x\right ) + \log \left (5 \, x + \log \left (-\frac {x - 6}{x}\right )\right )\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.74, size = 24, normalized size = 0.96 \begin {gather*} \log {\left (- 5 x \log {\left (x \right )} + \log {\left (5 x + \log {\left (\frac {6 - x}{x} \right )} \right )} \right )} - \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.69, size = 28, normalized size = 1.12 \begin {gather*} \log \left (-5 \, x \log \left (x\right ) + \log \left (5 \, x - \log \left (x\right ) + \log \left (-x + 6\right )\right )\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.64, size = 27, normalized size = 1.08 \begin {gather*} \ln \left (\ln \left (5\,x+\ln \left (-\frac {x-6}{x}\right )\right )-5\,x\,\ln \left (x\right )\right )-\ln \left (\ln \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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