Optimal. Leaf size=24 \[ \log ^4(3) (x+4 \log (\log (5)+\log ((5-x) (-1+x) x))) \]
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Rubi [A] time = 0.71, antiderivative size = 29, normalized size of antiderivative = 1.21, number of steps used = 5, number of rules used = 4, integrand size = 114, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6688, 12, 6728, 6684} \begin {gather*} 4 \log ^4(3) \log \left (\log \left (-x \left (x^2-6 x+5\right )\right )+\log (5)\right )+x \log ^4(3) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6688
Rule 6728
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\log ^4(3) \left (20-6 x^2 (-2+\log (5))+x^3 \log (5)+x (-48+5 \log (5))+x \left (5-6 x+x^2\right ) \log \left (-x \left (5-6 x+x^2\right )\right )\right )}{x \left (5-6 x+x^2\right ) \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )} \, dx\\ &=\log ^4(3) \int \frac {20-6 x^2 (-2+\log (5))+x^3 \log (5)+x (-48+5 \log (5))+x \left (5-6 x+x^2\right ) \log \left (-x \left (5-6 x+x^2\right )\right )}{x \left (5-6 x+x^2\right ) \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )} \, dx\\ &=\log ^4(3) \int \left (1+\frac {4 \left (5-12 x+3 x^2\right )}{(-5+x) (-1+x) x \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )}\right ) \, dx\\ &=x \log ^4(3)+\left (4 \log ^4(3)\right ) \int \frac {5-12 x+3 x^2}{(-5+x) (-1+x) x \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )} \, dx\\ &=x \log ^4(3)+4 \log ^4(3) \log \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 25, normalized size = 1.04 \begin {gather*} \log ^4(3) \left (x+4 \log \left (\log (5)+\log \left (-x \left (5-6 x+x^2\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 32, normalized size = 1.33 \begin {gather*} x \log \relax (3)^{4} + 4 \, \log \relax (3)^{4} \log \left (\log \relax (5) + \log \left (-x^{3} + 6 \, x^{2} - 5 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 32, normalized size = 1.33 \begin {gather*} x \log \relax (3)^{4} + 4 \, \log \relax (3)^{4} \log \left (\log \relax (5) + \log \left (-x^{3} + 6 \, x^{2} - 5 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 33, normalized size = 1.38
method | result | size |
norman | \(x \ln \relax (3)^{4}+4 \ln \relax (3)^{4} \ln \left (\ln \left (-x^{3}+6 x^{2}-5 x \right )+\ln \relax (5)\right )\) | \(33\) |
risch | \(x \ln \relax (3)^{4}+4 \ln \relax (3)^{4} \ln \left (\ln \left (-x^{3}+6 x^{2}-5 x \right )+\ln \relax (5)\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 29, normalized size = 1.21 \begin {gather*} x \log \relax (3)^{4} + 4 \, \log \relax (3)^{4} \log \left (\log \relax (5) + \log \left (x - 1\right ) + \log \relax (x) + \log \left (-x + 5\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.83, size = 29, normalized size = 1.21 \begin {gather*} x\,{\ln \relax (3)}^4+4\,{\ln \relax (3)}^4\,\ln \left (\ln \left (-5\,x^3+30\,x^2-25\,x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 31, normalized size = 1.29 \begin {gather*} x \log {\relax (3 )}^{4} + 4 \log {\relax (3 )}^{4} \log {\left (\log {\left (- x^{3} + 6 x^{2} - 5 x \right )} + \log {\relax (5 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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