Optimal. Leaf size=26 \[ \frac {3 x^2}{e \log \left (\left (-4-x+\frac {5 (4+x)}{x}\right )^2\right )} \]
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Rubi [F] time = 0.75, 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 {-120 x-6 x^3+\left (-120 x-6 x^2+6 x^3\right ) \log \left (\frac {400+40 x-39 x^2-2 x^3+x^4}{x^2}\right )}{e \left (-20-x+x^2\right ) \log ^2\left (\frac {400+40 x-39 x^2-2 x^3+x^4}{x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-120 x-6 x^3+\left (-120 x-6 x^2+6 x^3\right ) \log \left (\frac {400+40 x-39 x^2-2 x^3+x^4}{x^2}\right )}{\left (-20-x+x^2\right ) \log ^2\left (\frac {400+40 x-39 x^2-2 x^3+x^4}{x^2}\right )} \, dx}{e}\\ &=\frac {\int \frac {6 x \left (20+x^2-\left (-20-x+x^2\right ) \log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )\right )}{\left (20+x-x^2\right ) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}\\ &=\frac {6 \int \frac {x \left (20+x^2-\left (-20-x+x^2\right ) \log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )\right )}{\left (20+x-x^2\right ) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}\\ &=\frac {6 \int \left (-\frac {x \left (20+x^2\right )}{(-5+x) (4+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}+\frac {x}{\log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}\right ) \, dx}{e}\\ &=-\frac {6 \int \frac {x \left (20+x^2\right )}{(-5+x) (4+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}+\frac {6 \int \frac {x}{\log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}\\ &=-\frac {6 \int \left (\frac {1}{\log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}+\frac {25}{(-5+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}+\frac {x}{\log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}+\frac {16}{(4+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )}\right ) \, dx}{e}+\frac {6 \int \frac {x}{\log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}\\ &=-\frac {6 \int \frac {1}{\log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}-\frac {6 \int \frac {x}{\log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}+\frac {6 \int \frac {x}{\log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}-\frac {96 \int \frac {1}{(4+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}-\frac {150 \int \frac {1}{(-5+x) \log ^2\left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \, dx}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 25, normalized size = 0.96 \begin {gather*} \frac {3 x^2}{e \log \left (\frac {\left (20+x-x^2\right )^2}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 32, normalized size = 1.23 \begin {gather*} \frac {3 \, x^{2} e^{\left (-1\right )}}{\log \left (\frac {x^{4} - 2 \, x^{3} - 39 \, x^{2} + 40 \, x + 400}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 32, normalized size = 1.23 \begin {gather*} \frac {3 \, x^{2} e^{\left (-1\right )}}{\log \left (\frac {x^{4} - 2 \, x^{3} - 39 \, x^{2} + 40 \, x + 400}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.52, size = 33, normalized size = 1.27
method | result | size |
risch | \(\frac {3 x^{2} {\mathrm e}^{-1}}{\ln \left (\frac {x^{4}-2 x^{3}-39 x^{2}+40 x +400}{x^{2}}\right )}\) | \(33\) |
norman | \(\frac {3 x^{2} {\mathrm e}^{-1}}{\ln \left (\frac {x^{4}-2 x^{3}-39 x^{2}+40 x +400}{x^{2}}\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 22, normalized size = 0.85 \begin {gather*} \frac {3 \, x^{2} e^{\left (-1\right )}}{2 \, {\left (\log \left (x + 4\right ) + \log \left (x - 5\right ) - \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.20, size = 111, normalized size = 4.27 \begin {gather*} \frac {3\,x^2\,{\mathrm {e}}^{-1}+\frac {3\,x^2\,\ln \left (\frac {x^4-2\,x^3-39\,x^2+40\,x+400}{x^2}\right )\,{\mathrm {e}}^{-1}\,\left (-x^2+x+20\right )}{x^2+20}}{\ln \left (\frac {x^4-2\,x^3-39\,x^2+40\,x+400}{x^2}\right )}-3\,x\,{\mathrm {e}}^{-1}+3\,x^2\,{\mathrm {e}}^{-1}+\frac {60\,x+2400}{\mathrm {e}\,x^2+20\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 31, normalized size = 1.19 \begin {gather*} \frac {3 x^{2}}{e \log {\left (\frac {x^{4} - 2 x^{3} - 39 x^{2} + 40 x + 400}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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