Optimal. Leaf size=17 \[ \frac {3840}{(1-x) (-19+\log (4 x))^2} \]
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Rubi [F] time = 0.48, 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 {-7680-65280 x+3840 x \log (4 x)}{-6859 x+13718 x^2-6859 x^3+\left (1083 x-2166 x^2+1083 x^3\right ) \log (4 x)+\left (-57 x+114 x^2-57 x^3\right ) \log ^2(4 x)+\left (x-2 x^2+x^3\right ) \log ^3(4 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3840 (2+17 x-x \log (4 x))}{(1-x)^2 x (19-\log (4 x))^3} \, dx\\ &=3840 \int \frac {2+17 x-x \log (4 x)}{(1-x)^2 x (19-\log (4 x))^3} \, dx\\ &=3840 \int \left (\frac {2}{(-1+x) x (-19+\log (4 x))^3}+\frac {1}{(-1+x)^2 (-19+\log (4 x))^2}\right ) \, dx\\ &=3840 \int \frac {1}{(-1+x)^2 (-19+\log (4 x))^2} \, dx+7680 \int \frac {1}{(-1+x) x (-19+\log (4 x))^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 17, normalized size = 1.00 \begin {gather*} \frac {3840}{(1-x) (-19+\log (4 x))^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.94, size = 28, normalized size = 1.65 \begin {gather*} -\frac {3840}{{\left (x - 1\right )} \log \left (4 \, x\right )^{2} - 38 \, {\left (x - 1\right )} \log \left (4 \, x\right ) + 361 \, x - 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.26, size = 38, normalized size = 2.24 \begin {gather*} -\frac {3840}{x \log \left (4 \, x\right )^{2} - 38 \, x \log \left (4 \, x\right ) - \log \left (4 \, x\right )^{2} + 361 \, x + 38 \, \log \left (4 \, x\right ) - 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 16, normalized size = 0.94
method | result | size |
norman | \(-\frac {3840}{\left (\ln \left (4 x \right )-19\right )^{2} \left (x -1\right )}\) | \(16\) |
risch | \(-\frac {3840}{\left (\ln \left (4 x \right )-19\right )^{2} \left (x -1\right )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.49, size = 56, normalized size = 3.29 \begin {gather*} -\frac {3840}{{\left (x - 1\right )} \log \relax (x)^{2} + {\left (4 \, \log \relax (2)^{2} - 76 \, \log \relax (2) + 361\right )} x - 4 \, \log \relax (2)^{2} + 2 \, {\left (x {\left (2 \, \log \relax (2) - 19\right )} - 2 \, \log \relax (2) + 19\right )} \log \relax (x) + 76 \, \log \relax (2) - 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.85, size = 42, normalized size = 2.47 \begin {gather*} -\frac {\frac {3840\,{\ln \left (4\,x\right )}^2}{361}-\frac {7680\,\ln \left (4\,x\right )}{19}+3840}{{\left (\ln \left (4\,x\right )-19\right )}^2}-\frac {3840}{{\left (\ln \left (4\,x\right )-19\right )}^2\,\left (x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 27, normalized size = 1.59 \begin {gather*} - \frac {3840}{361 x + \left (38 - 38 x\right ) \log {\left (4 x \right )} + \left (x - 1\right ) \log {\left (4 x \right )}^{2} - 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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