Integrand size = 20, antiderivative size = 15 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{-9-25 \left (e^3-\frac {x}{4}\right )} \]
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Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.27, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2225} \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{\frac {1}{4} \left (25 x-4 \left (9+25 e^3\right )\right )} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {25}{4} \int e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx \\ & = e^{\frac {1}{4} \left (-4 \left (9+25 e^3\right )+25 x\right )} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{-9-25 e^3+\frac {25 x}{4}} \]
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Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73
method | result | size |
gosper | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
derivativedivides | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
default | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
norman | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
risch | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
parallelrisch | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
parts | \({\mathrm e}^{-25 \,{\mathrm e}^{3}+\frac {25 x}{4}-9}\) | \(11\) |
meijerg | \(-{\mathrm e}^{-25 \,{\mathrm e}^{3}-9} \left (1-{\mathrm e}^{\frac {25 x}{4}}\right )\) | \(18\) |
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Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{\left (\frac {25}{4} \, x - 25 \, e^{3} - 9\right )} \]
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Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{\frac {25 x}{4} - 25 e^{3} - 9} \]
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Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{\left (\frac {25}{4} \, x - 25 \, e^{3} - 9\right )} \]
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Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx=e^{\left (\frac {25}{4} \, x - 25 \, e^{3} - 9\right )} \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {25}{4} e^{\frac {1}{4} \left (-36-100 e^3+25 x\right )} \, dx={\mathrm {e}}^{-25\,{\mathrm {e}}^3}\,{\mathrm {e}}^{\frac {25\,x}{4}}\,{\mathrm {e}}^{-9} \]
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