Optimal. Leaf size=33 \[ \frac {1}{3} x \log \left (\frac {4+e^9+x \left (-x+x^2\right )}{x+\log \left (\frac {x}{-2+x}\right )}\right ) \]
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Rubi [F] time = 21.27, 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 {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+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 \frac {-8-8 x+6 x^2-4 x^3+5 x^4-2 x^5-e^9 \left (2+2 x-x^2\right )-x^2 \left (4-8 x+3 x^2\right ) \log \left (\frac {x}{-2+x}\right )-\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{3 \left (2 \left (4+e^9\right )-\left (4+e^9\right ) x-2 x^2+3 x^3-x^4\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx\\ &=\frac {1}{3} \int \frac {-8-8 x+6 x^2-4 x^3+5 x^4-2 x^5-e^9 \left (2+2 x-x^2\right )-x^2 \left (4-8 x+3 x^2\right ) \log \left (\frac {x}{-2+x}\right )-\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{\left (2 \left (4+e^9\right )-\left (4+e^9\right ) x-2 x^2+3 x^3-x^4\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx\\ &=\frac {1}{3} \int \left (\frac {8}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}+\frac {8 x}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}-\frac {6 x^2}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}+\frac {4 x^3}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}-\frac {5 x^4}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}+\frac {2 x^5}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}-\frac {e^9 \left (-2-2 x+x^2\right )}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}+\frac {x^2 (-2+3 x) \log \left (\frac {x}{-2+x}\right )}{\left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )}+\log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )\right ) \, dx\\ &=\frac {1}{3} \int \frac {x^2 (-2+3 x) \log \left (\frac {x}{-2+x}\right )}{\left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx+\frac {1}{3} \int \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right ) \, dx+\frac {2}{3} \int \frac {x^5}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx+\frac {4}{3} \int \frac {x^3}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx-\frac {5}{3} \int \frac {x^4}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx-2 \int \frac {x^2}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx+\frac {8}{3} \int \frac {1}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx+\frac {8}{3} \int \frac {x}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx-\frac {1}{3} e^9 \int \frac {-2-2 x+x^2}{(-2+x) \left (4+e^9-x^2+x^3\right ) \left (x+\log \left (\frac {x}{-2+x}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 32, normalized size = 0.97 \begin {gather*} \frac {1}{3} x \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{3} \, x \log \left (\frac {x^{3} - x^{2} + e^{9} + 4}{x + \log \left (\frac {x}{x - 2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, x^{5} - 5 \, x^{4} + 4 \, x^{3} - 6 \, x^{2} - {\left (x^{2} - 2 \, x - 2\right )} e^{9} + {\left (x^{5} - 3 \, x^{4} + 2 \, x^{3} + 4 \, x^{2} + {\left (x^{2} - 2 \, x\right )} e^{9} + {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2} + {\left (x - 2\right )} e^{9} + 4 \, x - 8\right )} \log \left (\frac {x}{x - 2}\right ) - 8 \, x\right )} \log \left (\frac {x^{3} - x^{2} + e^{9} + 4}{x + \log \left (\frac {x}{x - 2}\right )}\right ) + {\left (3 \, x^{4} - 8 \, x^{3} + 4 \, x^{2}\right )} \log \left (\frac {x}{x - 2}\right ) + 8 \, x + 8}{3 \, {\left (x^{5} - 3 \, x^{4} + 2 \, x^{3} + 4 \, x^{2} + {\left (x^{2} - 2 \, x\right )} e^{9} + {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2} + {\left (x - 2\right )} e^{9} + 4 \, x - 8\right )} \log \left (\frac {x}{x - 2}\right ) - 8 \, x\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.38, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (x -2\right ) {\mathrm e}^{9}+x^{4}-3 x^{3}+2 x^{2}+4 x -8\right ) \ln \left (\frac {x}{x -2}\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{9}+x^{5}-3 x^{4}+2 x^{3}+4 x^{2}-8 x \right ) \ln \left (\frac {{\mathrm e}^{9}+x^{3}-x^{2}+4}{\ln \left (\frac {x}{x -2}\right )+x}\right )+\left (3 x^{4}-8 x^{3}+4 x^{2}\right ) \ln \left (\frac {x}{x -2}\right )+\left (-x^{2}+2 x +2\right ) {\mathrm e}^{9}+2 x^{5}-5 x^{4}+4 x^{3}-6 x^{2}+8 x +8}{\left (\left (3 x -6\right ) {\mathrm e}^{9}+3 x^{4}-9 x^{3}+6 x^{2}+12 x -24\right ) \ln \left (\frac {x}{x -2}\right )+\left (3 x^{2}-6 x \right ) {\mathrm e}^{9}+3 x^{5}-9 x^{4}+6 x^{3}+12 x^{2}-24 x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 31, normalized size = 0.94 \begin {gather*} \frac {1}{3} \, x \log \left (x^{3} - x^{2} + e^{9} + 4\right ) - \frac {1}{3} \, x \log \left (x - \log \left (x - 2\right ) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.47, size = 29, normalized size = 0.88 \begin {gather*} \frac {x\,\ln \left (\frac {x^3-x^2+{\mathrm {e}}^9+4}{x+\ln \left (\frac {x}{x-2}\right )}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: CoercionFailed} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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