Integrand size = 27, antiderivative size = 12 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{-5-x+\frac {x}{e^{35}}} \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2259, 2234} \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{-\frac {5 e^{35}-\left (1-e^{35}\right ) x}{e^{35}}} \]
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Rule 12
Rule 2234
Rule 2259
Rubi steps \begin{align*} \text {integral}& = \left (1-e^{35}\right ) \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \, dx \\ & = \left (1-e^{35}\right ) \int e^{-35+\frac {-5 e^{35}+\left (1-e^{35}\right ) x}{e^{35}}} \, dx \\ & = e^{-\frac {5 e^{35}-\left (1-e^{35}\right ) x}{e^{35}}} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(25\) vs. \(2(12)=24\).
Time = 0.05 (sec) , antiderivative size = 25, normalized size of antiderivative = 2.08 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=-\frac {e^{-40+\left (-1+\frac {1}{e^{35}}\right ) x} \left (-1+e^{35}\right )}{-1+\frac {1}{e^{35}}} \]
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Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.42
method | result | size |
derivativedivides | \({\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}}\) | \(17\) |
default | \({\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}}\) | \(17\) |
norman | \({\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}}\) | \(17\) |
gosper | \({\mathrm e}^{-\left ({\mathrm e}^{35} x +5 \,{\mathrm e}^{35}-x \right ) {\mathrm e}^{-35}}\) | \(20\) |
parallelrisch | \(-\frac {\left (-{\mathrm e}^{35}+1\right ) {\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}}}{{\mathrm e}^{35}-1}\) | \(31\) |
meijerg | \(-\frac {{\mathrm e}^{30} \left (1-{\mathrm e}^{-x \left ({\mathrm e}^{35}-1\right ) {\mathrm e}^{-35}}\right )}{{\mathrm e}^{35}-1}+\frac {{\mathrm e}^{-5} \left (1-{\mathrm e}^{-x \left ({\mathrm e}^{35}-1\right ) {\mathrm e}^{-35}}\right )}{{\mathrm e}^{35}-1}\) | \(49\) |
risch | \(\frac {{\mathrm e}^{-\left ({\mathrm e}^{35} x +5 \,{\mathrm e}^{35}-x \right ) {\mathrm e}^{-35}} {\mathrm e}^{35}}{{\mathrm e}^{35}-1}-\frac {{\mathrm e}^{-\left ({\mathrm e}^{35} x +5 \,{\mathrm e}^{35}-x \right ) {\mathrm e}^{-35}}}{{\mathrm e}^{35}-1}\) | \(53\) |
parts | \(-\frac {{\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}} {\mathrm e}^{35}}{-{\mathrm e}^{35}+1}+\frac {{\mathrm e}^{\left (\left (-x -5\right ) {\mathrm e}^{35}+x \right ) {\mathrm e}^{-35}}}{-{\mathrm e}^{35}+1}\) | \(55\) |
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Time = 0.30 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.42 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{\left (-{\left ({\left (x + 40\right )} e^{35} - x\right )} e^{\left (-35\right )} + 35\right )} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{\frac {x + \left (- x - 5\right ) e^{35}}{e^{35}}} \]
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Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{\left (-{\left ({\left (x + 5\right )} e^{35} - x\right )} e^{\left (-35\right )}\right )} \]
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Time = 0.28 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx=e^{\left (-{\left ({\left (x + 5\right )} e^{35} - x\right )} e^{\left (-35\right )}\right )} \]
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Time = 13.56 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int e^{-35+\frac {e^{35} (-5-x)+x}{e^{35}}} \left (1-e^{35}\right ) \, dx={\mathrm {e}}^{-x}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-35}} \]
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