Integrand size = 31, antiderivative size = 19 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=5+e^{-8-\frac {2 \left (7-e^{10}\right )}{x}}+x \]
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Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {14, 2240} \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=x+e^{-\frac {2 \left (7-e^{10}\right )}{x}-8} \]
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Rule 14
Rule 2240
Rubi steps \begin{align*} \text {integral}& = \int \left (1+\frac {2 e^{-8+\frac {-14+2 e^{10}}{x}} \left (7-e^{10}\right )}{x^2}\right ) \, dx \\ & = x+\left (2 \left (7-e^{10}\right )\right ) \int \frac {e^{-8+\frac {-14+2 e^{10}}{x}}}{x^2} \, dx \\ & = e^{-8-\frac {2 \left (7-e^{10}\right )}{x}}+x \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}}+x \]
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Time = 0.14 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84
method | result | size |
risch | \({\mathrm e}^{\frac {2 \,{\mathrm e}^{10}-8 x -14}{x}}+x\) | \(16\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}-8 x -14}{x}}}{x}\) | \(27\) |
parts | \(x -\frac {\left (-2 \,{\mathrm e}^{10}+14\right ) {\mathrm e}^{\frac {2 \,{\mathrm e}^{10}-8 x -14}{x}}}{2 \left ({\mathrm e}^{10}-7\right )}\) | \(37\) |
derivativedivides | \(x +{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}}{x}-8-\frac {14}{x}}\) | \(39\) |
default | \(x +{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}}{x}-8-\frac {14}{x}}\) | \(39\) |
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none
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=x + e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=x + e^{\frac {2 \left (- 4 x - 7 + e^{10}\right )}{x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 47 vs. \(2 (15) = 30\).
Time = 0.21 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.47 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=x + \frac {e^{\left (\frac {2 \, e^{10}}{x} - \frac {14}{x} + 2\right )}}{e^{10} - 7} - \frac {7 \, e^{\left (\frac {2 \, e^{10}}{x} - \frac {14}{x} - 8\right )}}{e^{10} - 7} \]
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Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (15) = 30\).
Time = 0.32 (sec) , antiderivative size = 129, normalized size of antiderivative = 6.79 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=\frac {\frac {{\left (4 \, x - e^{10} + 7\right )} e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x} + 10\right )}}{x} - \frac {7 \, {\left (4 \, x - e^{10} + 7\right )} e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )}}{x} - e^{20} + 14 \, e^{10} - 4 \, e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x} + 10\right )} + 28 \, e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )} - 49}{{\left (\frac {4 \, x - e^{10} + 7}{x} - 4\right )} {\left (e^{10} - 7\right )}} \]
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Time = 9.49 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}} \left (14-2 e^{10}\right )+x^2}{x^2} \, dx=x+{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{10}}{x}}\,{\mathrm {e}}^{-8}\,{\mathrm {e}}^{-\frac {14}{x}} \]
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