Integrand size = 21, antiderivative size = 23 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=-16+e^3+e^{3-\frac {e^5+x}{x}}+\log ^2(2) \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.52, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2257, 2240} \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{2-\frac {e^5}{x}} \]
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Rule 2240
Rule 2257
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{7-\frac {e^5}{x}}}{x^2} \, dx \\ & = e^{2-\frac {e^5}{x}} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.52 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{2-\frac {e^5}{x}} \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57
method | result | size |
gosper | \({\mathrm e}^{-\frac {{\mathrm e}^{5}-2 x}{x}}\) | \(13\) |
risch | \({\mathrm e}^{-\frac {{\mathrm e}^{5}-2 x}{x}}\) | \(13\) |
parallelrisch | \({\mathrm e}^{-\frac {{\mathrm e}^{5}-2 x}{x}}\) | \(13\) |
derivativedivides | \({\mathrm e}^{\frac {-{\mathrm e}^{5}+2 x}{x}}\) | \(14\) |
default | \({\mathrm e}^{\frac {-{\mathrm e}^{5}+2 x}{x}}\) | \(14\) |
norman | \({\mathrm e}^{\frac {-{\mathrm e}^{5}+2 x}{x}}\) | \(14\) |
meijerg | \(-{\mathrm e}^{2} \left (1-{\mathrm e}^{-\frac {{\mathrm e}^{5}}{x}}\right )\) | \(17\) |
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none
Time = 0.23 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{\left (\frac {7 \, x - e^{5}}{x} - 5\right )} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.35 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{\frac {2 x - e^{5}}{x}} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.43 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{\left (-\frac {e^{5}}{x} + 2\right )} \]
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none
Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.43 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx=e^{\left (-\frac {e^{5}}{x} + 2\right )} \]
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Time = 11.42 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.48 \[ \int \frac {e^{5+\frac {-e^5+2 x}{x}}}{x^2} \, dx={\mathrm {e}}^{-\frac {{\mathrm {e}}^5}{x}}\,{\mathrm {e}}^2 \]
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