Integrand size = 5, antiderivative size = 18 \[ \int \left (3+e^2\right ) \, dx=3 (-5+x)+\log \left (\frac {3 e^{e^2 x}}{4}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {8} \[ \int \left (3+e^2\right ) \, dx=\left (3+e^2\right ) x \]
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Rule 8
Rubi steps \begin{align*} \text {integral}& = \left (3+e^2\right ) x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int \left (3+e^2\right ) \, dx=3 x+e^2 x \]
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Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39
method | result | size |
default | \(x \left ({\mathrm e}^{2}+3\right )\) | \(7\) |
norman | \(x \left ({\mathrm e}^{2}+3\right )\) | \(7\) |
parallelrisch | \(x \left ({\mathrm e}^{2}+3\right )\) | \(7\) |
risch | \({\mathrm e}^{2} x +3 x\) | \(9\) |
parts | \({\mathrm e}^{2} x +3 x\) | \(9\) |
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none
Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44 \[ \int \left (3+e^2\right ) \, dx=x e^{2} + 3 \, x \]
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Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.28 \[ \int \left (3+e^2\right ) \, dx=x \left (3 + e^{2}\right ) \]
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none
Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x {\left (e^{2} + 3\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x {\left (e^{2} + 3\right )} \]
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Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x\,\left ({\mathrm {e}}^2+3\right ) \]
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