Integrand size = 9, antiderivative size = 15 \[ \int \frac {-10+e^2}{e^2} \, dx=x-\frac {10 x-\log (3)}{e^2} \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \[ \int \frac {-10+e^2}{e^2} \, dx=-\frac {\left (10-e^2\right ) x}{e^2} \]
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Rule 8
Rubi steps \begin{align*} \text {integral}& = -\frac {\left (10-e^2\right ) x}{e^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {-10+e^2}{e^2} \, dx=x-\frac {10 x}{e^2} \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87
method | result | size |
default | \(\left ({\mathrm e}^{2}-10\right ) {\mathrm e}^{-2} x\) | \(13\) |
norman | \(\left ({\mathrm e}^{2}-10\right ) {\mathrm e}^{-2} x\) | \(13\) |
risch | \({\mathrm e}^{-2} x \,{\mathrm e}^{2}-10 \,{\mathrm e}^{-2} x\) | \(13\) |
parallelrisch | \(\left ({\mathrm e}^{2}-10\right ) {\mathrm e}^{-2} x\) | \(13\) |
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none
Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-10+e^2}{e^2} \, dx={\left (x e^{2} - 10 \, x\right )} e^{\left (-2\right )} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {-10+e^2}{e^2} \, dx=\frac {x \left (-10 + e^{2}\right )}{e^{2}} \]
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none
Time = 0.18 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {-10+e^2}{e^2} \, dx=x {\left (e^{2} - 10\right )} e^{\left (-2\right )} \]
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none
Time = 0.29 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {-10+e^2}{e^2} \, dx=x {\left (e^{2} - 10\right )} e^{\left (-2\right )} \]
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Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {-10+e^2}{e^2} \, dx=x\,{\mathrm {e}}^{-2}\,\left ({\mathrm {e}}^2-10\right ) \]
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