Integrand size = 15, antiderivative size = 22 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx=3-\frac {2 \left (1+e^5\right ) \left (3+e^x\right )}{e^5}+e^x x \]
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Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2218, 2207, 2225} \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx=-e^{x-5} \left (-e^5 x+e^5+2\right )-e^x \]
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Rule 2207
Rule 2218
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \int e^{-5+x} \left (-2-e^5+e^5 x\right ) \, dx \\ & = -e^{-5+x} \left (2+e^5-e^5 x\right )-e^5 \int e^{-5+x} \, dx \\ & = -e^x-e^{-5+x} \left (2+e^5-e^5 x\right ) \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx=e^x \left (-2-\frac {2}{e^5}+x\right ) \]
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Time = 0.06 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73
method | result | size |
risch | \(\left (x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{5}-2\right ) {\mathrm e}^{-5+x}\) | \(16\) |
gosper | \({\mathrm e}^{x} \left (x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{5}-2\right ) {\mathrm e}^{-5}\) | \(18\) |
norman | \({\mathrm e}^{x} x -2 \left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{-5} {\mathrm e}^{x}\) | \(18\) |
parts | \({\mathrm e}^{x} x -2 \,{\mathrm e}^{x}-2 \,{\mathrm e}^{-5} {\mathrm e}^{x}\) | \(18\) |
parallelrisch | \({\mathrm e}^{-5} \left (x \,{\mathrm e}^{5} {\mathrm e}^{x}-2 \,{\mathrm e}^{5} {\mathrm e}^{x}-2 \,{\mathrm e}^{x}\right )\) | \(23\) |
meijerg | \(2 \,{\mathrm e}^{-5} \left (1-{\mathrm e}^{x}\right )+2-{\mathrm e}^{x}-\frac {\left (2-2 x \right ) {\mathrm e}^{x}}{2}\) | \(26\) |
default | \({\mathrm e}^{-5} \left ({\mathrm e}^{5} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-{\mathrm e}^{5} {\mathrm e}^{x}-2 \,{\mathrm e}^{x}\right )\) | \(29\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx={\left ({\left (x - 2\right )} e^{5} - 2\right )} e^{\left (x - 5\right )} \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx=\frac {\left (x e^{5} - 2 e^{5} - 2\right ) e^{x}}{e^{5}} \]
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none
Time = 0.18 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx={\left (x - 1\right )} e^{x} - 2 \, e^{\left (x - 5\right )} - e^{x} \]
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none
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx={\left (x - 2\right )} e^{x} - 2 \, e^{\left (x - 5\right )} \]
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Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int e^{-5+x} \left (-2+e^5 (-1+x)\right ) \, dx=-{\mathrm {e}}^{x-5}\,\left (2\,{\mathrm {e}}^5-x\,{\mathrm {e}}^5+2\right ) \]
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