Optimal. Leaf size=30 \[ \frac {1}{(4+2 x) \left (5 x+\frac {(x+(-2+x) x) \log (x)}{4 x}\right )^2} \]
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Rubi [F] time = 1.89, 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 {32-656 x-496 x^2+\left (-24 x-24 x^2\right ) \log (x)}{32000 x^4+32000 x^5+8000 x^6+\left (-4800 x^3+3600 x^5+1200 x^6\right ) \log (x)+\left (240 x^2-240 x^3-180 x^4+120 x^5+60 x^6\right ) \log ^2(x)+\left (-4 x+8 x^2-x^3-5 x^4+x^5+x^6\right ) \log ^3(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 {8 \left (4-82 x-62 x^2-3 x (1+x) \log (x)\right )}{x (2+x)^2 (20 x+(-1+x) \log (x))^3} \, dx\\ &=8 \int \frac {4-82 x-62 x^2-3 x (1+x) \log (x)}{x (2+x)^2 (20 x+(-1+x) \log (x))^3} \, dx\\ &=8 \int \left (-\frac {2 \left (1-22 x+x^2\right )}{(-1+x) x (2+x) (20 x-\log (x)+x \log (x))^3}-\frac {3 (1+x)}{(-1+x) (2+x)^2 (20 x-\log (x)+x \log (x))^2}\right ) \, dx\\ &=-\left (16 \int \frac {1-22 x+x^2}{(-1+x) x (2+x) (20 x-\log (x)+x \log (x))^3} \, dx\right )-24 \int \frac {1+x}{(-1+x) (2+x)^2 (20 x-\log (x)+x \log (x))^2} \, dx\\ &=-\left (16 \int \left (-\frac {20}{3 (-1+x) (20 x-\log (x)+x \log (x))^3}-\frac {1}{2 x (20 x-\log (x)+x \log (x))^3}+\frac {49}{6 (2+x) (20 x-\log (x)+x \log (x))^3}\right ) \, dx\right )-24 \int \left (\frac {2}{9 (-1+x) (20 x-\log (x)+x \log (x))^2}+\frac {1}{3 (2+x)^2 (20 x-\log (x)+x \log (x))^2}-\frac {2}{9 (2+x) (20 x-\log (x)+x \log (x))^2}\right ) \, dx\\ &=-\left (\frac {16}{3} \int \frac {1}{(-1+x) (20 x-\log (x)+x \log (x))^2} \, dx\right )+\frac {16}{3} \int \frac {1}{(2+x) (20 x-\log (x)+x \log (x))^2} \, dx+8 \int \frac {1}{x (20 x-\log (x)+x \log (x))^3} \, dx-8 \int \frac {1}{(2+x)^2 (20 x-\log (x)+x \log (x))^2} \, dx+\frac {320}{3} \int \frac {1}{(-1+x) (20 x-\log (x)+x \log (x))^3} \, dx-\frac {392}{3} \int \frac {1}{(2+x) (20 x-\log (x)+x \log (x))^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.84, size = 19, normalized size = 0.63 \begin {gather*} \frac {8}{(2+x) (20 x+(-1+x) \log (x))^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 42, normalized size = 1.40 \begin {gather*} \frac {8}{400 \, x^{3} + {\left (x^{3} - 3 \, x + 2\right )} \log \relax (x)^{2} + 800 \, x^{2} + 40 \, {\left (x^{3} + x^{2} - 2 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.21, size = 114, normalized size = 3.80 \begin {gather*} \frac {8 \, {\left (x^{2} - 22 \, x + 1\right )}}{x^{5} \log \relax (x)^{2} + 40 \, x^{5} \log \relax (x) - 22 \, x^{4} \log \relax (x)^{2} + 400 \, x^{5} - 840 \, x^{4} \log \relax (x) - 2 \, x^{3} \log \relax (x)^{2} - 8000 \, x^{4} - 920 \, x^{3} \log \relax (x) + 68 \, x^{2} \log \relax (x)^{2} - 17200 \, x^{3} + 1800 \, x^{2} \log \relax (x) - 47 \, x \log \relax (x)^{2} + 800 \, x^{2} - 80 \, x \log \relax (x) + 2 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 22, normalized size = 0.73
method | result | size |
risch | \(\frac {8}{\left (2+x \right ) \left (x \ln \relax (x )+20 x -\ln \relax (x )\right )^{2}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 42, normalized size = 1.40 \begin {gather*} \frac {8}{400 \, x^{3} + {\left (x^{3} - 3 \, x + 2\right )} \log \relax (x)^{2} + 800 \, x^{2} + 40 \, {\left (x^{3} + x^{2} - 2 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.33, size = 62, normalized size = 2.07 \begin {gather*} \frac {8\,\left (x^4-20\,x^3-43\,x^2+2\,x\right )}{{\left (x+2\right )}^2\,\left (400\,x^2+{\ln \relax (x)}^2\,{\left (x-1\right )}^2+40\,x\,\ln \relax (x)\,\left (x-1\right )\right )\,\left (x^3-22\,x^2+x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 41, normalized size = 1.37 \begin {gather*} \frac {8}{400 x^{3} + 800 x^{2} + \left (x^{3} - 3 x + 2\right ) \log {\relax (x )}^{2} + \left (40 x^{3} + 40 x^{2} - 80 x\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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