Integrand size = 13, antiderivative size = 14 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=-2+\frac {2 e^{5 x}}{13}-3 x \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2225} \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=\frac {2 e^{5 x}}{13}-3 x \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{13} \int \left (-39+10 e^{5 x}\right ) \, dx \\ & = -3 x+\frac {10}{13} \int e^{5 x} \, dx \\ & = \frac {2 e^{5 x}}{13}-3 x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=\frac {2 e^{5 x}}{13}-3 x \]
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Time = 0.08 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79
method | result | size |
default | \(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\) | \(11\) |
norman | \(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\) | \(11\) |
risch | \(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\) | \(11\) |
parallelrisch | \(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\) | \(11\) |
parts | \(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\) | \(11\) |
derivativedivides | \(\frac {2 \,{\mathrm e}^{5 x}}{13}-\frac {3 \ln \left ({\mathrm e}^{5 x}\right )}{5}\) | \(15\) |
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Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=-3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=- 3 x + \frac {2 e^{5 x}}{13} \]
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Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=-3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \]
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Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=-3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{13} \left (-39+10 e^{5 x}\right ) \, dx=\frac {2\,{\mathrm {e}}^{5\,x}}{13}-3\,x \]
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