Integrand size = 9, antiderivative size = 11 \[ \int e^{1+x^2} x \, dx=\frac {e^{1+x^2}}{2} \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2240} \[ \int e^{1+x^2} x \, dx=\frac {e^{x^2+1}}{2} \]
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Rule 2240
Rubi steps \begin{align*} \text {integral}& = \frac {e^{1+x^2}}{2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int e^{1+x^2} x \, dx=\frac {e^{1+x^2}}{2} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82
method | result | size |
gosper | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
derivativedivides | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
default | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
risch | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
parallelrisch | \(\frac {{\mathrm e}^{x^{2}+1}}{2}\) | \(9\) |
meijerg | \(-\frac {{\mathrm e} \left (1-{\mathrm e}^{x^{2}}\right )}{2}\) | \(13\) |
parts | \(\frac {{\mathrm e} \,\operatorname {erfi}\left (x \right ) \sqrt {\pi }\, x}{2}-\frac {{\mathrm e} \left (x \,\operatorname {erfi}\left (x \right ) \sqrt {\pi }-{\mathrm e}^{x^{2}}\right )}{2}\) | \(30\) |
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none
Time = 0.28 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^2} x \, dx=\frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int e^{1+x^2} x \, dx=\frac {e^{x^{2} + 1}}{2} \]
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none
Time = 0.21 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^2} x \, dx=\frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]
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none
Time = 0.31 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^2} x \, dx=\frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^2} x \, dx=\frac {{\mathrm {e}}^{x^2}\,\mathrm {e}}{2} \]
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