Integrand size = 141, antiderivative size = 30 \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=2+e^{e^{e^{x^2 \left (-\frac {4 e^6}{1-x}+x\right )}} x^2} \]
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\[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=\int \frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{(-1+x)^2} \, dx \\ & = \int \left (2 \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x+\frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^3 \left (-8 e^6+\left (3+4 e^6\right ) x-6 x^2+3 x^3\right )}{(1-x)^2}\right ) \, dx \\ & = 2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+\int \frac {\exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^3 \left (-8 e^6+\left (3+4 e^6\right ) x-6 x^2+3 x^3\right )}{(1-x)^2} \, dx \\ & = 2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+\int \left (-4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )-\frac {4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{(-1+x)^2}-\frac {8 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{-1+x}+4 \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^2+3 \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^4\right ) \, dx \\ & = 2 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2\right ) x \, dx+3 \int \exp \left (e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^4 \, dx-4 \int \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) \, dx-4 \int \frac {\exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{(-1+x)^2} \, dx+4 \int \exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right ) x^2 \, dx-8 \int \frac {\exp \left (6+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2+\frac {4 e^6 x^2}{-1+x}+x^3\right )}{-1+x} \, dx \\ \end{align*}
Time = 0.38 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=e^{e^{e^{x^2 \left (\frac {4 e^6}{-1+x}+x\right )}} x^2} \]
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Time = 254.99 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
method | result | size |
risch | \({\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{\frac {x^{2} \left (x^{2}+4 \,{\mathrm e}^{6}-x \right )}{-1+x}}}}\) | \(28\) |
parallelrisch | \({\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{\frac {x^{2} \left (x^{2}+4 \,{\mathrm e}^{6}-x \right )}{-1+x}}}}\) | \(30\) |
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Timed out. \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=\text {Timed out} \]
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Time = 0.63 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=e^{\left (x^{2} e^{\left (e^{\left (x^{3} + 4 \, x e^{6} + \frac {4 \, e^{6}}{x - 1} + 4 \, e^{6}\right )}\right )}\right )} \]
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\[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx=\int { \frac {{\left (2 \, x^{3} - 4 \, x^{2} + {\left (3 \, x^{6} - 6 \, x^{5} + 3 \, x^{4} + 4 \, {\left (x^{4} - 2 \, x^{3}\right )} e^{6}\right )} e^{\left (\frac {x^{4} - x^{3} + 4 \, x^{2} e^{6}}{x - 1}\right )} + 2 \, x\right )} e^{\left (x^{2} e^{\left (e^{\left (\frac {x^{4} - x^{3} + 4 \, x^{2} e^{6}}{x - 1}\right )}\right )} + e^{\left (\frac {x^{4} - x^{3} + 4 \, x^{2} e^{6}}{x - 1}\right )}\right )}}{x^{2} - 2 \, x + 1} \,d x } \]
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Time = 9.24 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37 \[ \int \frac {e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}+e^{e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}}} x^2} \left (2 x-4 x^2+2 x^3+e^{\frac {4 e^6 x^2-x^3+x^4}{-1+x}} \left (3 x^4-6 x^5+3 x^6+e^6 \left (-8 x^3+4 x^4\right )\right )\right )}{1-2 x+x^2} \, dx={\mathrm {e}}^{x^2\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^6}{x-1}}\,{\mathrm {e}}^{\frac {x^4}{x-1}}\,{\mathrm {e}}^{-\frac {x^3}{x-1}}}} \]
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