Integrand size = 28, antiderivative size = 21 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {e^{1-e^4+e^{e^4}+x^2}}{x} \]
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Time = 0.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {2326} \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {e^{x^2+e^{e^4}-e^4+1}}{x} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {e^{1-e^4+e^{e^4}+x^2}}{x} \\ \end{align*}
Time = 0.34 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {e^{1-e^4+e^{e^4}+x^2}}{x} \]
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Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86
method | result | size |
gosper | \({\mathrm e}^{-\ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{4}}-{\mathrm e}^{4}+x^{2}+1}\) | \(18\) |
norman | \({\mathrm e}^{-\ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{4}}-{\mathrm e}^{4}+x^{2}+1}\) | \(18\) |
risch | \(\frac {{\mathrm e}^{1+{\mathrm e}^{{\mathrm e}^{4}}-{\mathrm e}^{4}+x^{2}}}{x}\) | \(18\) |
parallelrisch | \({\mathrm e}^{-\ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{4}}-{\mathrm e}^{4}+x^{2}+1}\) | \(18\) |
default | \({\mathrm e} \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4}}} {\mathrm e}^{-{\mathrm e}^{4}} \sqrt {\pi }\, \operatorname {erfi}\left (x \right )-{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4}}} {\mathrm e}^{-{\mathrm e}^{4}} \left (-\frac {{\mathrm e}^{x^{2}}}{x}+\sqrt {\pi }\, \operatorname {erfi}\left (x \right )\right )\) | \(48\) |
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none
Time = 0.32 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=e^{\left (x^{2} - e^{4} + e^{\left (e^{4}\right )} - \log \left (x\right ) + 1\right )} \]
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Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {e^{x^{2} - e^{4} + 1 + e^{e^{4}}}}{x} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.33 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=-i \, \sqrt {\pi } \operatorname {erf}\left (i \, x\right ) e^{\left (-e^{4} + e^{\left (e^{4}\right )} + 1\right )} + \frac {\sqrt {-x^{2}} e^{\left (-e^{4} + e^{\left (e^{4}\right )} + 1\right )} \Gamma \left (-\frac {1}{2}, -x^{2}\right )}{2 \, x} \]
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none
Time = 0.29 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {e^{\left (x^{2} - e^{4} + e^{\left (e^{4}\right )} + 1\right )}}{x} \]
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Time = 12.46 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {e^{1-e^4+e^{e^4}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx=\frac {{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^4}}\,{\mathrm {e}}^{x^2}\,\mathrm {e}}{x} \]
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