Integrand size = 9, antiderivative size = 19 \[ \int \frac {e^{x^2}}{x^2} \, dx=-\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x) \]
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Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2245, 2235} \[ \int \frac {e^{x^2}}{x^2} \, dx=\sqrt {\pi } \text {erfi}(x)-\frac {e^{x^2}}{x} \]
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Rule 2235
Rule 2245
Rubi steps \begin{align*} \text {integral}& = -\frac {e^{x^2}}{x}+2 \int e^{x^2} \, dx \\ & = -\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {e^{x^2}}{x^2} \, dx=-\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x) \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89
method | result | size |
default | \(-\frac {{\mathrm e}^{x^{2}}}{x}+\operatorname {erfi}\left (x \right ) \sqrt {\pi }\) | \(17\) |
risch | \(-\frac {{\mathrm e}^{x^{2}}}{x}+\operatorname {erfi}\left (x \right ) \sqrt {\pi }\) | \(17\) |
meijerg | \(\frac {i \left (\frac {2 i {\mathrm e}^{x^{2}}}{x}-2 i \operatorname {erfi}\left (x \right ) \sqrt {\pi }\right )}{2}\) | \(23\) |
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none
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {e^{x^2}}{x^2} \, dx=\frac {\sqrt {\pi } x \operatorname {erfi}\left (x\right ) - e^{\left (x^{2}\right )}}{x} \]
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Time = 0.15 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {e^{x^2}}{x^2} \, dx=\sqrt {\pi } \operatorname {erfi}{\left (x \right )} - \frac {e^{x^{2}}}{x} \]
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none
Time = 0.21 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {e^{x^2}}{x^2} \, dx=-\frac {\sqrt {-x^{2}} \Gamma \left (-\frac {1}{2}, -x^{2}\right )}{2 \, x} \]
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\[ \int \frac {e^{x^2}}{x^2} \, dx=\int { \frac {e^{\left (x^{2}\right )}}{x^{2}} \,d x } \]
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Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{x^2}}{x^2} \, dx=-\frac {{\mathrm {e}}^{x^2}}{x}+\sqrt {\pi }\,\mathrm {erfc}\left (x\,1{}\mathrm {i}\right )\,1{}\mathrm {i} \]
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