Optimal. Leaf size=33 \[ \left (9-e^x+x\right )^2 \left (-x-\log (x)+\frac {\log (x)}{1-x^2}\right )^2 \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A] time = 0.17, size = 32, normalized size = 0.97 \begin {gather*} \frac {x^2 \left (9-e^x+x\right )^2 \left (-1+x^2+x \log (x)\right )^2}{\left (-1+x^2\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 200, normalized size = 6.06 \begin {gather*} \frac {x^{8} + 18 \, x^{7} + 79 \, x^{6} - 36 \, x^{5} - 161 \, x^{4} + 18 \, x^{3} + {\left (x^{6} + 18 \, x^{5} + x^{4} e^{\left (2 \, x\right )} + 81 \, x^{4} - 2 \, {\left (x^{5} + 9 \, x^{4}\right )} e^{x}\right )} \log \relax (x)^{2} + 81 \, x^{2} + {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + 9 \, x^{2}\right )} e^{x} + 2 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 18 \, x^{4} - 81 \, x^{3} + {\left (x^{5} - x^{3}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} e^{x}\right )} \log \relax (x)}{x^{4} - 2 \, x^{2} + 1} \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 \, {\left (2 \, x^{9} + 28 \, x^{8} + 93 \, x^{7} - 2 \, x^{6} - 273 \, x^{5} - 80 \, x^{4} + 259 \, x^{3} + {\left (x^{7} + 9 \, x^{6} - 3 \, x^{5} - 45 \, x^{4} - 162 \, x^{3} + {\left (x^{6} - x^{4} - 2 \, x^{3}\right )} e^{\left (2 \, x\right )} - {\left (x^{7} + 10 \, x^{6} - x^{5} - 14 \, x^{4} - 36 \, x^{3}\right )} e^{x}\right )} \log \relax (x)^{2} + 54 \, x^{2} + {\left (x^{8} + x^{7} - 2 \, x^{6} - 3 \, x^{5} + x^{4} + 3 \, x^{3} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{9} + 12 \, x^{8} + 17 \, x^{7} - 18 \, x^{6} - 55 \, x^{5} + 55 \, x^{3} + 6 \, x^{2} - 18 \, x\right )} e^{x} + {\left (3 \, x^{8} + 37 \, x^{7} + 91 \, x^{6} - 28 \, x^{5} - 337 \, x^{4} - 9 \, x^{3} + 243 \, x^{2} + {\left (2 \, x^{7} + x^{6} - 3 \, x^{5} - 4 \, x^{4} + x^{3} + 3 \, x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{8} + 11 \, x^{7} + 8 \, x^{6} - 15 \, x^{5} - 36 \, x^{4} + 4 \, x^{3} + 27 \, x^{2}\right )} e^{x}\right )} \log \relax (x) - 81 \, x\right )}}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.12, size = 130, normalized size = 3.94
method | result | size |
risch | \(\frac {\left (x^{2}-2 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}+18 x -18 \,{\mathrm e}^{x}+81\right ) x^{4} \ln \relax (x )^{2}}{\left (x^{2}-1\right )^{2}}+\frac {2 \left (x^{5}-2 \,{\mathrm e}^{x} x^{4}+{\mathrm e}^{2 x} x^{3}+18 x^{4}-18 \,{\mathrm e}^{x} x^{3}+81 x^{3}-18 x^{2}+18\right ) \ln \relax (x )}{x^{2}-1}+x^{4}-2 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x} x^{2}+18 x^{3}-18 \,{\mathrm e}^{x} x^{2}+81 x^{2}+36 \ln \relax (x )\) | \(130\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.73, size = 436, normalized size = 13.21 \begin {gather*} x^{4} + \frac {56}{3} \, x^{3} + 99 \, x^{2} + 164 \, x - \frac {2 \, x^{7} + 54 \, x^{6} + 488 \, x^{5} - 108 \, x^{4} - 982 \, x^{3} - 3 \, {\left (x^{6} + 18 \, x^{5} + 81 \, x^{4}\right )} \log \relax (x)^{2} + 54 \, x^{2} - 3 \, {\left (x^{6} + x^{4} \log \relax (x)^{2} - 2 \, x^{4} + x^{2} + 2 \, {\left (x^{5} - x^{3}\right )} \log \relax (x)\right )} e^{\left (2 \, x\right )} + 6 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + {\left (x^{5} + 9 \, x^{4}\right )} \log \relax (x)^{2} + 9 \, x^{2} + 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} \log \relax (x)\right )} e^{x} - 6 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 36 \, x^{4} - 81 \, x^{3} + 36 \, x^{2} - 18\right )} \log \relax (x) + 492 \, x}{3 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {7 \, {\left (13 \, x^{3} - 11 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} + \frac {9 \, x^{3} - 7 \, x}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {20 \, {\left (5 \, x^{3} - 3 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} - \frac {27 \, {\left (x^{3} + x\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {8 \, x^{2} - 7}{x^{4} - 2 \, x^{2} + 1} - \frac {93 \, {\left (6 \, x^{2} - 5\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {273 \, {\left (4 \, x^{2} - 3\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {259 \, {\left (2 \, x^{2} - 1\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {81}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + 18 \, \log \left (x^{2} - 1\right ) - 18 \, \log \left (x + 1\right ) - 18 \, \log \left (x - 1\right ) + 36 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.06, size = 316, normalized size = 9.58 \begin {gather*} 81\,{\ln \relax (x)}^2-2\,x^3\,{\mathrm {e}}^x-18\,x^2\,{\mathrm {e}}^x-\frac {81\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+x^2\,{\mathrm {e}}^{2\,x}+81\,x^2+18\,x^3+x^4+{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2+\frac {162\,x^2\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {18\,x^5\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {x^6\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {162\,x^3\,\ln \relax (x)}{x^2-1}+\frac {36\,x^4\,\ln \relax (x)}{x^2-1}+\frac {2\,x^5\,\ln \relax (x)}{x^2-1}-\frac {18\,x^4\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {2\,x^5\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {36\,x^3\,{\mathrm {e}}^x\,\ln \relax (x)}{x^2-1}-\frac {4\,x^4\,{\mathrm {e}}^x\,\ln \relax (x)}{x^2-1}+\frac {2\,x^3\,{\mathrm {e}}^{2\,x}\,\ln \relax (x)}{x^2-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.96, size = 369, normalized size = 11.18 \begin {gather*} x^{4} + 18 x^{3} + 81 x^{2} + \frac {\left (x^{10} + 2 x^{9} \log {\relax (x )} + x^{8} \log {\relax (x )}^{2} - 4 x^{8} - 6 x^{7} \log {\relax (x )} - 2 x^{6} \log {\relax (x )}^{2} + 6 x^{6} + 6 x^{5} \log {\relax (x )} + x^{4} \log {\relax (x )}^{2} - 4 x^{4} - 2 x^{3} \log {\relax (x )} + x^{2}\right ) e^{2 x} + \left (- 2 x^{11} - 4 x^{10} \log {\relax (x )} - 18 x^{10} - 2 x^{9} \log {\relax (x )}^{2} - 36 x^{9} \log {\relax (x )} + 8 x^{9} - 18 x^{8} \log {\relax (x )}^{2} + 12 x^{8} \log {\relax (x )} + 72 x^{8} + 4 x^{7} \log {\relax (x )}^{2} + 108 x^{7} \log {\relax (x )} - 12 x^{7} + 36 x^{6} \log {\relax (x )}^{2} - 12 x^{6} \log {\relax (x )} - 108 x^{6} - 2 x^{5} \log {\relax (x )}^{2} - 108 x^{5} \log {\relax (x )} + 8 x^{5} - 18 x^{4} \log {\relax (x )}^{2} + 4 x^{4} \log {\relax (x )} + 72 x^{4} + 36 x^{3} \log {\relax (x )} - 2 x^{3} - 18 x^{2}\right ) e^{x}}{x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1} + 36 \log {\relax (x )} + \frac {\left (x^{6} + 18 x^{5} + 81 x^{4}\right ) \log {\relax (x )}^{2}}{x^{4} - 2 x^{2} + 1} + \frac {\left (2 x^{5} + 36 x^{4} + 162 x^{3} - 36 x^{2} + 36\right ) \log {\relax (x )}}{x^{2} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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