Integrand size = 18, antiderivative size = 24 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {2 \left (e^{\frac {20+x}{x}}+\left (3-e^{32}\right ) x\right )}{x} \]
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Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2326} \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=-\frac {40 e^{\frac {x+20}{x}}}{x^3 \left (\frac {1}{x}-\frac {x+20}{x^2}\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = -\frac {40 e^{\frac {20+x}{x}}}{x^3 \left (\frac {1}{x}-\frac {20+x}{x^2}\right )} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {2 e^{1+\frac {20}{x}}}{x} \]
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Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
norman | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
risch | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
parallelrisch | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
derivativedivides | \(\frac {\left (1+\frac {20}{x}\right ) {\mathrm e}^{1+\frac {20}{x}}}{10}-\frac {{\mathrm e}^{1+\frac {20}{x}}}{10}\) | \(29\) |
default | \(\frac {\left (1+\frac {20}{x}\right ) {\mathrm e}^{1+\frac {20}{x}}}{10}-\frac {{\mathrm e}^{1+\frac {20}{x}}}{10}\) | \(29\) |
meijerg | \(-\frac {{\mathrm e} \left (1-{\mathrm e}^{\frac {20}{x}}\right )}{10}+\frac {{\mathrm e} \left (1-\frac {\left (2-\frac {40}{x}\right ) {\mathrm e}^{\frac {20}{x}}}{2}\right )}{10}\) | \(37\) |
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none
Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.54 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {2 \, e^{\left (\frac {x + 20}{x}\right )}}{x} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.33 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {2 e^{\frac {x + 20}{x}}}{x} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=-\frac {1}{10} \, e \Gamma \left (2, -\frac {20}{x}\right ) + \frac {1}{10} \, e^{\left (\frac {20}{x} + 1\right )} \]
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none
Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {{\left (x + 20\right )} e^{\left (\frac {x + 20}{x}\right )}}{10 \, x} - \frac {1}{10} \, e^{\left (\frac {x + 20}{x}\right )} \]
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Time = 13.60 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.54 \[ \int \frac {e^{\frac {20+x}{x}} (-40-2 x)}{x^3} \, dx=\frac {2\,\mathrm {e}\,{\mathrm {e}}^{20/x}}{x} \]
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