Integrand size = 18, antiderivative size = 30 \[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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Time = 0.02 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6525} \[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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Rule 6525
Rubi steps \begin{align*} \text {integral}& = \frac {2 b x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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\[\int \frac {\operatorname {erfi}\left (b x \right ) {\mathrm e}^{-b^{2} x^{2}}}{x}d x\]
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\[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x} \,d x } \]
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Time = 3.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\frac {2 b x {{}_{2}F_{2}\left (\begin {matrix} \frac {1}{2}, 1 \\ \frac {3}{2}, \frac {3}{2} \end {matrix}\middle | {- b^{2} x^{2}} \right )}}{\sqrt {\pi }} \]
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\[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x} \,d x } \]
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\[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x} \,d x } \]
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Timed out. \[ \int \frac {e^{-b^2 x^2} \text {erfi}(b x)}{x} \, dx=\int \frac {{\mathrm {e}}^{-b^2\,x^2}\,\mathrm {erfi}\left (b\,x\right )}{x} \,d x \]
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