Optimal. Leaf size=18 \[ \frac {16 x}{3969 \log ^2\left (x-\frac {x}{-4+x}\right )} \]
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Rubi [F] time = 0.42, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-640+256 x-32 x^2+\left (320-144 x+16 x^2\right ) \log \left (\frac {-5 x+x^2}{-4+x}\right )}{\left (79380-35721 x+3969 x^2\right ) \log ^3\left (\frac {-5 x+x^2}{-4+x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {32 \left (20-8 x+x^2\right )}{3969 (-5+x) (-4+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )}+\frac {16}{3969 \log ^2\left (\frac {(-5+x) x}{-4+x}\right )}\right ) \, dx\\ &=\frac {16 \int \frac {1}{\log ^2\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}-\frac {32 \int \frac {20-8 x+x^2}{(-5+x) (-4+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}\\ &=\frac {16 \int \frac {1}{\log ^2\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}-\frac {32 \int \left (\frac {1}{\log ^3\left (\frac {(-5+x) x}{-4+x}\right )}+\frac {5}{(-5+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )}-\frac {4}{(-4+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )}\right ) \, dx}{3969}\\ &=\frac {16 \int \frac {1}{\log ^2\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}-\frac {32 \int \frac {1}{\log ^3\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}+\frac {128 \int \frac {1}{(-4+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}-\frac {160 \int \frac {1}{(-5+x) \log ^3\left (\frac {(-5+x) x}{-4+x}\right )} \, dx}{3969}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 18, normalized size = 1.00 \begin {gather*} \frac {16 x}{3969 \log ^2\left (\frac {(-5+x) x}{-4+x}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 19, normalized size = 1.06 \begin {gather*} \frac {16 \, x}{3969 \, \log \left (\frac {x^{2} - 5 \, x}{x - 4}\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.27, size = 74, normalized size = 4.11 \begin {gather*} \frac {16 \, {\left (x^{3} - 8 \, x^{2} + 20 \, x\right )}}{3969 \, {\left (x^{2} \log \left (\frac {x^{2} - 5 \, x}{x - 4}\right )^{2} - 8 \, x \log \left (\frac {x^{2} - 5 \, x}{x - 4}\right )^{2} + 20 \, \log \left (\frac {x^{2} - 5 \, x}{x - 4}\right )^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.25, size = 20, normalized size = 1.11
method | result | size |
norman | \(\frac {16 x}{3969 \ln \left (\frac {x^{2}-5 x}{x -4}\right )^{2}}\) | \(20\) |
risch | \(\frac {16 x}{3969 \ln \left (\frac {x^{2}-5 x}{x -4}\right )^{2}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.40, size = 49, normalized size = 2.72 \begin {gather*} -\frac {16 \, x}{3969 \, {\left (2 \, {\left (\log \left (x - 5\right ) + \log \relax (x)\right )} \log \left (x - 4\right ) - \log \left (x - 4\right )^{2} - \log \left (x - 5\right )^{2} - 2 \, \log \left (x - 5\right ) \log \relax (x) - \log \relax (x)^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 219, normalized size = 12.17 \begin {gather*} \frac {8\,x}{3969}+\frac {\frac {8\,x\,\left (x^2-9\,x+20\right )}{3969\,\left (x^2-8\,x+20\right )}-\frac {8\,x\,\ln \left (-\frac {5\,x-x^2}{x-4}\right )\,\left (x^2-9\,x+20\right )\,\left (x^4-16\,x^3+112\,x^2-360\,x+400\right )}{3969\,{\left (x^2-8\,x+20\right )}^3}}{\ln \left (-\frac {5\,x-x^2}{x-4}\right )}+\frac {\frac {16\,x}{3969}-\frac {8\,x\,\ln \left (-\frac {5\,x-x^2}{x-4}\right )\,\left (x^2-9\,x+20\right )}{3969\,\left (x^2-8\,x+20\right )}}{{\ln \left (-\frac {5\,x-x^2}{x-4}\right )}^2}+\frac {\frac {32\,x^4}{441}-\frac {5056\,x^3}{3969}+\frac {10240\,x^2}{1323}-\frac {25600\,x}{1323}+\frac {64000}{3969}}{x^6-24\,x^5+252\,x^4-1472\,x^3+5040\,x^2-9600\,x+8000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 17, normalized size = 0.94 \begin {gather*} \frac {16 x}{3969 \log {\left (\frac {x^{2} - 5 x}{x - 4} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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