Optimal. Leaf size=22 \[ \frac {3 x \left (-1+\frac {e x}{-x+\log (-4+x)}\right )}{\log (x)} \]
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Rubi [F] time = 5.59, 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 {-12 x^2+3 x^3+e \left (-12 x^2+3 x^3\right )+\left (24 x-6 x^2+e \left (12 x-3 x^2\right )\right ) \log (-4+x)+(-12+3 x) \log ^2(-4+x)+\left (12 x^2-3 x^3+e \left (9 x^2-3 x^3\right )+\left (-24 x+6 x^2+e \left (-24 x+6 x^2\right )\right ) \log (-4+x)+(12-3 x) \log ^2(-4+x)\right ) \log (x)}{\left (-4 x^2+x^3+\left (8 x-2 x^2\right ) \log (-4+x)+(-4+x) \log ^2(-4+x)\right ) \log ^2(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 {3 \left ((-4+x) \log ^2(-4+x) (-1+\log (x))-(-4+x) x \log (-4+x) (-2-e+2 (1+e) \log (x))+x^2 (-((1+e) (-4+x))+(-4+e (-3+x)+x) \log (x))\right )}{(4-x) (x-\log (-4+x))^2 \log ^2(x)} \, dx\\ &=3 \int \frac {(-4+x) \log ^2(-4+x) (-1+\log (x))-(-4+x) x \log (-4+x) (-2-e+2 (1+e) \log (x))+x^2 (-((1+e) (-4+x))+(-4+e (-3+x)+x) \log (x))}{(4-x) (x-\log (-4+x))^2 \log ^2(x)} \, dx\\ &=3 \int \left (\frac {(1+e) x-\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)}+\frac {-4 \left (1+\frac {3 e}{4}\right ) x^2+(1+e) x^3+8 (1+e) x \log (-4+x)-2 (1+e) x^2 \log (-4+x)-4 \log ^2(-4+x)+x \log ^2(-4+x)}{(4-x) (x-\log (-4+x))^2 \log (x)}\right ) \, dx\\ &=3 \int \frac {(1+e) x-\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)} \, dx+3 \int \frac {-4 \left (1+\frac {3 e}{4}\right ) x^2+(1+e) x^3+8 (1+e) x \log (-4+x)-2 (1+e) x^2 \log (-4+x)-4 \log ^2(-4+x)+x \log ^2(-4+x)}{(4-x) (x-\log (-4+x))^2 \log (x)} \, dx\\ &=3 \int \left (\frac {(1+e) x}{(x-\log (-4+x)) \log ^2(x)}-\frac {\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)}\right ) \, dx+3 \int \frac {x^2 (-4+e (-3+x)+x)-2 (1+e) (-4+x) x \log (-4+x)+(-4+x) \log ^2(-4+x)}{(4-x) (x-\log (-4+x))^2 \log (x)} \, dx\\ &=3 \int \left (\frac {4 \left (1+\frac {3 e}{4}\right ) x^2}{(-4+x) (x-\log (-4+x))^2 \log (x)}-\frac {(1+e) x^3}{(-4+x) (x-\log (-4+x))^2 \log (x)}-\frac {8 (1+e) x \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}+\frac {2 (1+e) x^2 \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}+\frac {4 \log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}-\frac {x \log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}\right ) \, dx-3 \int \frac {\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)} \, dx+(3 (1+e)) \int \frac {x}{(x-\log (-4+x)) \log ^2(x)} \, dx\\ &=-\left (3 \int \frac {\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)} \, dx\right )-3 \int \frac {x \log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx+12 \int \frac {\log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx+(3 (1+e)) \int \frac {x}{(x-\log (-4+x)) \log ^2(x)} \, dx-(3 (1+e)) \int \frac {x^3}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx+(6 (1+e)) \int \frac {x^2 \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx-(24 (1+e)) \int \frac {x \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx+(3 (4+3 e)) \int \frac {x^2}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx\\ &=-\left (3 \int \left (\frac {\log ^2(-4+x)}{(x-\log (-4+x))^2 \log (x)}+\frac {4 \log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}\right ) \, dx\right )-3 \int \frac {\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)} \, dx+12 \int \frac {\log ^2(-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx-(3 (1+e)) \int \left (\frac {16}{(x-\log (-4+x))^2 \log (x)}+\frac {64}{(-4+x) (x-\log (-4+x))^2 \log (x)}+\frac {4 x}{(x-\log (-4+x))^2 \log (x)}+\frac {x^2}{(x-\log (-4+x))^2 \log (x)}\right ) \, dx+(3 (1+e)) \int \frac {x}{(x-\log (-4+x)) \log ^2(x)} \, dx+(6 (1+e)) \int \left (\frac {4 \log (-4+x)}{(x-\log (-4+x))^2 \log (x)}+\frac {16 \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}+\frac {x \log (-4+x)}{(x-\log (-4+x))^2 \log (x)}\right ) \, dx-(24 (1+e)) \int \left (\frac {\log (-4+x)}{(x-\log (-4+x))^2 \log (x)}+\frac {4 \log (-4+x)}{(-4+x) (x-\log (-4+x))^2 \log (x)}\right ) \, dx+(3 (4+3 e)) \int \left (\frac {4}{(x-\log (-4+x))^2 \log (x)}+\frac {16}{(-4+x) (x-\log (-4+x))^2 \log (x)}+\frac {x}{(x-\log (-4+x))^2 \log (x)}\right ) \, dx\\ &=-\left (3 \int \frac {\log (-4+x)}{(x-\log (-4+x)) \log ^2(x)} \, dx\right )-3 \int \frac {\log ^2(-4+x)}{(x-\log (-4+x))^2 \log (x)} \, dx+(3 (1+e)) \int \frac {x}{(x-\log (-4+x)) \log ^2(x)} \, dx-(3 (1+e)) \int \frac {x^2}{(x-\log (-4+x))^2 \log (x)} \, dx+(6 (1+e)) \int \frac {x \log (-4+x)}{(x-\log (-4+x))^2 \log (x)} \, dx-(12 (1+e)) \int \frac {x}{(x-\log (-4+x))^2 \log (x)} \, dx-(48 (1+e)) \int \frac {1}{(x-\log (-4+x))^2 \log (x)} \, dx-(192 (1+e)) \int \frac {1}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx+(3 (4+3 e)) \int \frac {x}{(x-\log (-4+x))^2 \log (x)} \, dx+(12 (4+3 e)) \int \frac {1}{(x-\log (-4+x))^2 \log (x)} \, dx+(48 (4+3 e)) \int \frac {1}{(-4+x) (x-\log (-4+x))^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 28, normalized size = 1.27 \begin {gather*} -\frac {3 x (x+e x-\log (-4+x))}{(x-\log (-4+x)) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 33, normalized size = 1.50 \begin {gather*} -\frac {3 \, {\left (x^{2} e + x^{2} - x \log \left (x - 4\right )\right )}}{{\left (x - \log \left (x - 4\right )\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 34, normalized size = 1.55 \begin {gather*} -\frac {3 \, {\left (x^{2} e + x^{2} - x \log \left (x - 4\right )\right )}}{x \log \relax (x) - \log \left (x - 4\right ) \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 30, normalized size = 1.36
method | result | size |
risch | \(-\frac {3 x}{\ln \relax (x )}-\frac {3 \,{\mathrm e} x^{2}}{\ln \relax (x ) \left (x -\ln \left (x -4\right )\right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 33, normalized size = 1.50 \begin {gather*} -\frac {3 \, {\left (x^{2} {\left (e + 1\right )} - x \log \left (x - 4\right )\right )}}{x \log \relax (x) - \log \left (x - 4\right ) \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.37, size = 402, normalized size = 18.27 \begin {gather*} \frac {\frac {3\,x\,\ln \relax (x)\,\left (75\,x-100\,\mathrm {e}+60\,x\,\mathrm {e}-15\,x^2\,\mathrm {e}+x^3\,\mathrm {e}-15\,x^2+x^3-125\right )}{2\,{\left (x-5\right )}^3}-\frac {3\,x\,\left (20\,\mathrm {e}-10\,x-8\,x\,\mathrm {e}+x^2\,\mathrm {e}+x^2+25\right )}{2\,{\left (x-5\right )}^2}+\frac {3\,x\,{\ln \relax (x)}^2\,\left (75\,x-200\,\mathrm {e}+160\,x\,\mathrm {e}-30\,x^2\,\mathrm {e}+2\,x^3\,\mathrm {e}-15\,x^2+x^3-125\right )}{2\,{\left (x-5\right )}^3}}{\ln \relax (x)}+\frac {\frac {3\,x^2\,\left (4\,\mathrm {e}-x\,\mathrm {e}-3\,\mathrm {e}\,\ln \relax (x)+x\,\mathrm {e}\,\ln \relax (x)\right )}{{\ln \relax (x)}^2\,\left (x-5\right )}+\frac {3\,\ln \left (x-4\right )\,\left (x\,\mathrm {e}-2\,x\,\mathrm {e}\,\ln \relax (x)\right )\,\left (x-4\right )}{{\ln \relax (x)}^2\,\left (x-5\right )}}{x-\ln \left (x-4\right )}+\ln \relax (x)\,\left (45\,\mathrm {e}+\frac {45}{2}\right )-\frac {225\,x\,\mathrm {e}-75\,x^2\,\mathrm {e}}{2\,x^3-30\,x^2+150\,x-250}+\frac {\frac {3\,x\,\mathrm {e}\,\left (x-4\right )}{x-5}-\frac {3\,x\,\ln \relax (x)\,\left (60\,\mathrm {e}-10\,x-28\,x\,\mathrm {e}+3\,x^2\,\mathrm {e}+x^2+25\right )}{2\,{\left (x-5\right )}^2}+\frac {3\,x\,{\ln \relax (x)}^2\,\left (40\,\mathrm {e}-10\,x-20\,x\,\mathrm {e}+2\,x^2\,\mathrm {e}+x^2+25\right )}{2\,{\left (x-5\right )}^2}}{{\ln \relax (x)}^2}-x\,\left (\frac {9\,\mathrm {e}}{2}+3\right )+\frac {\ln \relax (x)\,\left (\left (-3\,\mathrm {e}-\frac {3}{2}\right )\,x^4+\left (435\,\mathrm {e}+225\right )\,x^2+\left (-3075\,\mathrm {e}-1500\right )\,x+5625\,\mathrm {e}+\frac {5625}{2}\right )}{x^3-15\,x^2+75\,x-125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 27, normalized size = 1.23 \begin {gather*} \frac {3 e x^{2}}{- x \log {\relax (x )} + \log {\relax (x )} \log {\left (x - 4 \right )}} - \frac {3 x}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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