Integrand size = 8, antiderivative size = 10 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25 x^2}{8 e^6} \]
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Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25 x^2}{8 e^6} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {25 \int x \, dx}{4 e^6} \\ & = \frac {25 x^2}{8 e^6} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25 x^2}{8 e^6} \]
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Time = 0.11 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80
method | result | size |
risch | \(\frac {25 x^{2} {\mathrm e}^{-6}}{8}\) | \(8\) |
default | \(\frac {25 x^{2} {\mathrm e}^{-6}}{8}\) | \(10\) |
norman | \(\frac {25 x^{2} {\mathrm e}^{-6}}{8}\) | \(10\) |
gosper | \(\frac {25 \,{\mathrm e}^{-2 x -6} x^{2} {\mathrm e}^{2 x}}{8}\) | \(16\) |
parallelrisch | \(\frac {25 \,{\mathrm e}^{-2 x -6} x^{2} {\mathrm e}^{2 x}}{8}\) | \(16\) |
meijerg | \(\frac {25 \,{\mathrm e}^{2 x -6+2 x \,{\mathrm e}^{-6}} {\mathrm e}^{-4 x} \left (1-\frac {\left (2-4 x \left (1-{\mathrm e}^{-6}\right )\right ) {\mathrm e}^{2 x \left (1-{\mathrm e}^{-6}\right )}}{2}\right )}{16 \left (1-{\mathrm e}^{-6}\right )^{2}}\) | \(53\) |
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Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25}{8} \, x^{2} e^{\left (-6\right )} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25 x^{2}}{8 e^{6}} \]
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Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25}{8} \, x^{2} e^{\left (-6\right )} \]
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Time = 0.29 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25}{8} \, x^{2} e^{\left (-6\right )} \]
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Time = 15.15 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {25 x}{4 e^6} \, dx=\frac {25\,x^2\,{\mathrm {e}}^{-6}}{8} \]
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