Integrand size = 333, antiderivative size = 34 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {e^{\left (3-3 \left (-e^{4 x}+x+x^2\right )\right )^2}}{1+\log \left (3-e^x+x\right )} \]
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\[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\int \frac {\exp \left (9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )\right ) \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+\exp \left (9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )\right ) \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-55-72 e^{8 x} \left (-3+e^x-x\right )-72 x+144 x^2+162 x^3+36 x^4+18 e^{4 x} \left (-3+e^x-x\right ) \left (-3+6 x+4 x^2\right )-e^x \left (-19-18 x+54 x^2+36 x^3\right )-18 \left (3+4 e^{8 x} \left (-3+e^x-x\right )+4 x-8 x^2-9 x^3-2 x^4-e^{4 x} \left (-3+e^x-x\right ) \left (-3+6 x+4 x^2\right )+e^x \left (-1-x+3 x^2+2 x^3\right )\right ) \log \left (3-e^x+x\right )\right )}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx \\ & = \int \left (\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} (2+x)}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}+\frac {72 e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )}-\frac {18 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-3+6 x+4 x^2\right )}{1+\log \left (3-e^x+x\right )}+\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3-18 \log \left (3-e^x+x\right )-18 x \log \left (3-e^x+x\right )+54 x^2 \log \left (3-e^x+x\right )+36 x^3 \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2}\right ) \, dx \\ & = -\left (18 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-3+6 x+4 x^2\right )}{1+\log \left (3-e^x+x\right )} \, dx\right )+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} (2+x)}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3-18 \log \left (3-e^x+x\right )-18 x \log \left (3-e^x+x\right )+54 x^2 \log \left (3-e^x+x\right )+36 x^3 \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx \\ & = -\left (18 \int \left (-\frac {3 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )}+\frac {6 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )}+\frac {4 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )}\right ) \, dx\right )+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3+18 \left (-1-x+3 x^2+2 x^3\right ) \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \left (-\frac {2 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \left (-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2}+\frac {18 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-1-x+3 x^2+2 x^3\right )}{1+\log \left (3-e^x+x\right )}\right ) \, dx \\ & = -\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-1-x+3 x^2+2 x^3\right )}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \left (\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{-1-\log \left (3-e^x+x\right )}-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )}+\frac {3 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )}+\frac {2 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^3}{1+\log \left (3-e^x+x\right )}\right ) \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{-1-\log \left (3-e^x+x\right )} \, dx-18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx+36 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^3}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx \\ \end{align*}
Time = 0.29 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.97 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \]
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Time = 22.39 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.71
method | result | size |
parallelrisch | \(\frac {{\mathrm e}^{9 \,{\mathrm e}^{8 x}+\left (-18 x^{2}-18 x +18\right ) {\mathrm e}^{4 x}+9 x^{4}+18 x^{3}-9 x^{2}-18 x +9}}{1+\ln \left (-{\mathrm e}^{x}+3+x \right )}\) | \(58\) |
risch | \(\frac {{\mathrm e}^{9 x^{4}-18 x^{2} {\mathrm e}^{4 x}+18 x^{3}-18 x \,{\mathrm e}^{4 x}-9 x^{2}+18 \,{\mathrm e}^{4 x}+9 \,{\mathrm e}^{8 x}-18 x +9}}{1+\ln \left (-{\mathrm e}^{x}+3+x \right )}\) | \(63\) |
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Time = 0.25 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.53 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )}}{\log \left (x - e^{x} + 3\right ) + 1} \]
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Time = 1.02 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.56 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {e^{9 x^{4} + 18 x^{3} - 9 x^{2} - 18 x + \left (- 18 x^{2} - 18 x + 18\right ) e^{4 x} + 9 e^{8 x} + 9}}{\log {\left (x - e^{x} + 3 \right )} + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (30) = 60\).
Time = 0.61 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.38 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {e^{\left (9 \, x^{4} + 18 \, x^{3} - 18 \, x^{2} e^{\left (4 \, x\right )} + 9 \, e^{\left (8 \, x\right )} + 18 \, e^{\left (4 \, x\right )} + 9\right )}}{e^{\left (9 \, x^{2} + 18 \, x e^{\left (4 \, x\right )} + 18 \, x\right )} \log \left (x - e^{x} + 3\right ) + e^{\left (9 \, x^{2} + 18 \, x e^{\left (4 \, x\right )} + 18 \, x\right )}} \]
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\[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\int { \frac {18 \, {\left (2 \, x^{4} + 9 \, x^{3} + 8 \, x^{2} + 4 \, {\left (x - e^{x} + 3\right )} e^{\left (8 \, x\right )} - {\left (4 \, x^{3} + 18 \, x^{2} - {\left (4 \, x^{2} + 6 \, x - 3\right )} e^{x} + 15 \, x - 9\right )} e^{\left (4 \, x\right )} - {\left (2 \, x^{3} + 3 \, x^{2} - x - 1\right )} e^{x} - 4 \, x - 3\right )} e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )} \log \left (x - e^{x} + 3\right ) + {\left (36 \, x^{4} + 162 \, x^{3} + 144 \, x^{2} + 72 \, {\left (x - e^{x} + 3\right )} e^{\left (8 \, x\right )} - 18 \, {\left (4 \, x^{3} + 18 \, x^{2} - {\left (4 \, x^{2} + 6 \, x - 3\right )} e^{x} + 15 \, x - 9\right )} e^{\left (4 \, x\right )} - {\left (36 \, x^{3} + 54 \, x^{2} - 18 \, x - 19\right )} e^{x} - 72 \, x - 55\right )} e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )}}{{\left (x - e^{x} + 3\right )} \log \left (x - e^{x} + 3\right )^{2} + 2 \, {\left (x - e^{x} + 3\right )} \log \left (x - e^{x} + 3\right ) + x - e^{x} + 3} \,d x } \]
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Time = 8.71 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.03 \[ \int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )} \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx=\frac {{\mathrm {e}}^{9\,{\mathrm {e}}^{8\,x}}\,{\mathrm {e}}^{18\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-18\,x}\,{\mathrm {e}}^9\,{\mathrm {e}}^{-18\,x\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-9\,x^2}\,{\mathrm {e}}^{9\,x^4}\,{\mathrm {e}}^{18\,x^3}\,{\mathrm {e}}^{-18\,x^2\,{\mathrm {e}}^{4\,x}}}{\ln \left (x-{\mathrm {e}}^x+3\right )+1} \]
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