Integrand size = 158, antiderivative size = 34 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=e^{\frac {4}{3} \left (-2+e^{x/2}-x+x^2\right ) \left (-3+\frac {3}{-e^x+x}\right )} \]
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\[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=\int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{\left (e^x-x\right )^2} \, dx \\ & = \int \left (-2 \exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )-4 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) (-1+2 x)+\frac {4 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) (-1+x) \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2}+\frac {2 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (-2+e^{x/2}-6 x+2 x^2\right )}{e^x-x}\right ) \, dx \\ & = -\left (2 \int \exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \, dx\right )+2 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (-2+e^{x/2}-6 x+2 x^2\right )}{e^x-x} \, dx-4 \int \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) (-1+2 x) \, dx+4 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) (-1+x) \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2} \, dx \\ & = -\left (2 \int \exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \, dx\right )+2 \int \left (-\frac {2 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )}{e^x-x}+\frac {\exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )}{e^x-x}-\frac {6 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x}{e^x-x}+\frac {2 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x^2}{e^x-x}\right ) \, dx-4 \int \left (-\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )+2 \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x\right ) \, dx+4 \int \left (-\frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2}+\frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2}\right ) \, dx \\ & = -\left (2 \int \exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \, dx\right )+2 \int \frac {\exp \left (\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )}{e^x-x} \, dx+4 \int \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \, dx-4 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right )}{e^x-x} \, dx+4 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x^2}{e^x-x} \, dx-4 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2} \, dx+4 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x \left (-2+e^{x/2}-x+x^2\right )}{\left (e^x-x\right )^2} \, dx-8 \int \exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x \, dx-12 \int \frac {\exp \left (\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}\right ) x}{e^x-x} \, dx \\ & = -\left (2 \int e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \, dx\right )+2 \int \frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{e^x-x} \, dx+4 \int e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \, dx-4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{e^x-x} \, dx+4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^2}{e^x-x} \, dx-4 \int \left (-\frac {2 e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{\left (e^x-x\right )^2}+\frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{\left (e^x-x\right )^2}-\frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2}+\frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^2}{\left (e^x-x\right )^2}\right ) \, dx+4 \int \left (-\frac {2 e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2}+\frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2}-\frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^2}{\left (e^x-x\right )^2}+\frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^3}{\left (e^x-x\right )^2}\right ) \, dx-8 \int e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x \, dx-12 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{e^x-x} \, dx \\ & = -\left (2 \int e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \, dx\right )+2 \int \frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{e^x-x} \, dx+4 \int e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \, dx-4 \int \frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{\left (e^x-x\right )^2} \, dx-4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{e^x-x} \, dx+4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2} \, dx+4 \int \frac {e^{\frac {x}{2}+\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2} \, dx-2 \left (4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^2}{\left (e^x-x\right )^2} \, dx\right )+4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^2}{e^x-x} \, dx+4 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x^3}{\left (e^x-x\right )^2} \, dx+8 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}}}{\left (e^x-x\right )^2} \, dx-8 \int e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x \, dx-8 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{\left (e^x-x\right )^2} \, dx-12 \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} x}{e^x-x} \, dx \\ \end{align*}
Time = 0.29 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=e^{-\frac {4 \left (1+e^x-x\right ) \left (-2+e^{x/2}-x+x^2\right )}{e^x-x}} \]
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Time = 3.32 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.91
method | result | size |
risch | \({\mathrm e}^{-\frac {4 \left (x^{2}+{\mathrm e}^{\frac {x}{2}}-x -2\right ) \left (1+{\mathrm e}^{x}-x \right )}{{\mathrm e}^{x}-x}}\) | \(31\) |
parallelrisch | \({\mathrm e}^{\frac {\left (-4 \,{\mathrm e}^{\frac {x}{2}}-4 x^{2}+4 x +8\right ) {\mathrm e}^{x}+\left (-4+4 x \right ) {\mathrm e}^{\frac {x}{2}}+4 x^{3}-8 x^{2}-4 x +8}{{\mathrm e}^{x}-x}}\) | \(59\) |
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Time = 0.25 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=e^{\left (-\frac {4 \, {\left (x^{3} - 2 \, x^{2} + {\left (x - 1\right )} e^{\left (\frac {1}{2} \, x\right )} - {\left (x^{2} - x - 2\right )} e^{x} - x - e^{\left (\frac {3}{2} \, x\right )} + 2\right )}}{x - e^{x}}\right )} \]
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Time = 0.38 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=e^{\frac {4 x^{3} - 8 x^{2} - 4 x + \left (4 x - 4\right ) e^{\frac {x}{2}} + \left (- 4 x^{2} + 4 x - 4 e^{\frac {x}{2}} + 8\right ) e^{x} + 8}{- x + e^{x}}} \]
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\[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=\int { -\frac {2 \, {\left (4 \, x^{3} - 4 \, x^{2} + {\left (4 \, x + e^{\left (\frac {1}{2} \, x\right )} - 2\right )} e^{\left (2 \, x\right )} + {\left (x^{2} - x + 2\right )} e^{\left (\frac {1}{2} \, x\right )} - {\left (10 \, x^{2} + {\left (2 \, x + 1\right )} e^{\left (\frac {1}{2} \, x\right )} - 10 \, x - 2\right )} e^{x} - 4\right )} e^{\left (-\frac {4 \, {\left (x^{3} - 2 \, x^{2} + {\left (x - 1\right )} e^{\left (\frac {1}{2} \, x\right )} - {\left (x^{2} - x + e^{\left (\frac {1}{2} \, x\right )} - 2\right )} e^{x} - x + 2\right )}}{x - e^{x}}\right )}}{x^{2} - 2 \, x e^{x} + e^{\left (2 \, x\right )}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (25) = 50\).
Time = 1.11 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.68 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx=e^{\left (-\frac {4 \, {\left (x^{3} - x^{2} e^{x} - 2 \, x^{2} + x e^{\left (\frac {1}{2} \, x\right )} + x e^{x} - x - e^{\left (\frac {3}{2} \, x\right )} - e^{\left (\frac {1}{2} \, x\right )} + 2 \, e^{x} + 2\right )}}{x - e^{x}}\right )} \]
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Time = 12.43 (sec) , antiderivative size = 143, normalized size of antiderivative = 4.21 \[ \int \frac {e^{\frac {8-4 x-8 x^2+4 x^3+e^{x/2} (-4+4 x)+e^x \left (8-4 e^{x/2}+4 x-4 x^2\right )}{e^x-x}} \left (8+e^{2 x} \left (4-2 e^{x/2}-8 x\right )+8 x^2-8 x^3+e^{x/2} \left (-4+2 x-2 x^2\right )+e^x \left (-4-20 x+20 x^2+e^{x/2} (2+4 x)\right )\right )}{e^{2 x}-2 e^x x+x^2} \, dx={\mathrm {e}}^{-\frac {4\,x^3}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {8\,x^2}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {8\,{\mathrm {e}}^x}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {8}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{x/2}\,{\mathrm {e}}^x}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{x/2}}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^x}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {4\,x}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^{x/2}}{x-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^x}{x-{\mathrm {e}}^x}} \]
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