Integrand size = 29, antiderivative size = 20 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=3 \left (e^{4-\frac {x}{15}}-e^{-4+x} x\right ) \]
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Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.55, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 2225, 2207} \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=-3 e^{x-4} (x+1)+3 e^{\frac {60-x}{15}}+3 e^{x-4} \]
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Rule 12
Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx \\ & = -\left (\frac {1}{5} \int e^{\frac {60-x}{15}} \, dx\right )+\frac {1}{5} \int e^{-4+x} (-15-15 x) \, dx \\ & = 3 e^{\frac {60-x}{15}}-3 e^{-4+x} (1+x)+3 \int e^{-4+x} \, dx \\ & = 3 e^{\frac {60-x}{15}}+3 e^{-4+x}-3 e^{-4+x} (1+x) \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=3 e^{4-\frac {x}{15}}-3 e^{-4+x} x \]
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Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85
method | result | size |
risch | \(3 \,{\mathrm e}^{-\frac {x}{15}+4}-3 x \,{\mathrm e}^{x -4}\) | \(17\) |
parallelrisch | \(3 \,{\mathrm e}^{-\frac {x}{15}+4}-3 x \,{\mathrm e}^{x -4}\) | \(17\) |
default | \(-3 \,{\mathrm e}^{x -4} \left (x -4\right )-12 \,{\mathrm e}^{x -4}+3 \,{\mathrm e}^{-\frac {x}{15}+4}\) | \(25\) |
parts | \(-3 \,{\mathrm e}^{x -4} \left (x -4\right )-12 \,{\mathrm e}^{x -4}+3 \,{\mathrm e}^{-\frac {x}{15}+4}\) | \(25\) |
meijerg | \(3 \,{\mathrm e}^{-4} \left (1-{\mathrm e}^{x}\right )-3 \,{\mathrm e}^{-4} \left (1-\frac {\left (2-2 x \right ) {\mathrm e}^{x}}{2}\right )-3 \,{\mathrm e}^{4} \left (1-{\mathrm e}^{-\frac {x}{15}}\right )\) | \(39\) |
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Time = 0.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=-3 \, {\left (x e^{56} - e^{\left (-\frac {16}{15} \, x + 64\right )}\right )} e^{\left (x - 60\right )} \]
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Time = 0.15 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=- 3 x e^{56} e^{x - 60} + 3 e^{4 - \frac {x}{15}} \]
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Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=-3 \, {\left (x - 1\right )} e^{\left (x - 4\right )} - 3 \, e^{\left (x - 4\right )} + 3 \, e^{\left (-\frac {1}{15} \, x + 4\right )} \]
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Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=-3 \, x e^{\left (x - 4\right )} + 3 \, e^{\left (-\frac {1}{15} \, x + 4\right )} \]
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Time = 12.42 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{5} \left (-e^{\frac {60-x}{15}}+e^{-4+x} (-15-15 x)\right ) \, dx=3\,{\mathrm {e}}^{4-\frac {x}{15}}-3\,x\,{\mathrm {e}}^{x-4} \]
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