Integrand size = 19, antiderivative size = 32 \[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\frac {2 b e^c x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};b^2 x^2\right )}{\sqrt {\pi }} \]
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Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {6523} \[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\frac {2 b e^c x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};b^2 x^2\right )}{\sqrt {\pi }} \]
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Rule 6523
Rubi steps \begin{align*} \text {integral}& = \frac {2 b e^c x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};b^2 x^2\right )}{\sqrt {\pi }} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\frac {2 b e^c x \, _2F_2\left (\frac {1}{2},1;\frac {3}{2},\frac {3}{2};b^2 x^2\right )}{\sqrt {\pi }} \]
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\[\int \frac {{\mathrm e}^{b^{2} x^{2}+c} \operatorname {erf}\left (b x \right )}{x}d x\]
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\[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x} \,d x } \]
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Time = 5.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\frac {2 b x e^{c} {{}_{2}F_{2}\left (\begin {matrix} \frac {1}{2}, 1 \\ \frac {3}{2}, \frac {3}{2} \end {matrix}\middle | {b^{2} x^{2}} \right )}}{\sqrt {\pi }} \]
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\[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x} \,d x } \]
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\[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x} \,d x } \]
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Timed out. \[ \int \frac {e^{c+b^2 x^2} \text {erf}(b x)}{x} \, dx=\int \frac {{\mathrm {e}}^{b^2\,x^2+c}\,\mathrm {erf}\left (b\,x\right )}{x} \,d x \]
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