Integrand size = 50, antiderivative size = 25 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=e^{-4-2 e \left (-8-\frac {4}{x}+\frac {e^x}{x}\right )}-x \]
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Time = 0.35 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {14, 6838} \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=e^{-\frac {2 e^{x+1}}{x}+\frac {8 e}{x}-4 (1-4 e)}-x \]
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Rule 14
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \left (-1+\frac {2 e^{-3 \left (1-\frac {16 e}{3}\right )+\frac {8 e}{x}-\frac {2 e^{1+x}}{x}} \left (-4+e^x-e^x x\right )}{x^2}\right ) \, dx \\ & = -x+2 \int \frac {e^{-3 \left (1-\frac {16 e}{3}\right )+\frac {8 e}{x}-\frac {2 e^{1+x}}{x}} \left (-4+e^x-e^x x\right )}{x^2} \, dx \\ & = e^{-4 (1-4 e)+\frac {8 e}{x}-\frac {2 e^{1+x}}{x}}-x \\ \end{align*}
Time = 0.56 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=e^{-4+16 e+\frac {8 e}{x}-\frac {2 e^{1+x}}{x}}-x \]
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Time = 0.67 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12
method | result | size |
parallelrisch | \(-x +{\mathrm e}^{\frac {-2 \,{\mathrm e} \,{\mathrm e}^{x}+\left (16 x +8\right ) {\mathrm e}-4 x}{x}}\) | \(28\) |
risch | \(-x +{\mathrm e}^{\frac {16 x \,{\mathrm e}+8 \,{\mathrm e}-2 \,{\mathrm e}^{1+x}-4 x}{x}}\) | \(30\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {-2 \,{\mathrm e} \,{\mathrm e}^{x}+\left (16 x +8\right ) {\mathrm e}-4 x}{x}}-x^{2}}{x}\) | \(36\) |
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Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=-x + e^{\left (\frac {2 \, {\left (4 \, {\left (2 \, x + 1\right )} e - 2 \, x - e^{\left (x + 1\right )}\right )}}{x}\right )} \]
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Time = 0.16 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=- x + e^{\frac {- 4 x + e \left (16 x + 8\right ) - 2 e e^{x}}{x}} \]
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Time = 0.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=-x + e^{\left (\frac {8 \, e}{x} - \frac {2 \, e^{\left (x + 1\right )}}{x} + 16 \, e - 4\right )} \]
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Time = 0.35 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx=-x + e^{\left (\frac {8 \, e}{x} - \frac {2 \, e^{\left (x + 1\right )}}{x} + 16 \, e - 4\right )} \]
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Time = 17.08 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {-2 e^{1+x}-4 x+e (8+16 x)}{x}} \left (-8 e+e^{1+x} (2-2 x)\right )-x^2}{x^2} \, dx={\mathrm {e}}^{\frac {8\,\mathrm {e}}{x}}\,{\mathrm {e}}^{16\,\mathrm {e}}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{-\frac {2\,\mathrm {e}\,{\mathrm {e}}^x}{x}}-x \]
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