Integrand size = 8, antiderivative size = 32 \[ \int \frac {\text {erf}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6493} \[ \int \frac {\text {erf}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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Rule 6493
Rubi steps \begin{align*} \text {integral}& = \frac {2 b x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {\text {erf}(b x)}{x} \, dx=\frac {2 b x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};-b^2 x^2\right )}{\sqrt {\pi }} \]
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.72
method | result | size |
meijerg | \(\frac {2 b x \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {1}{2}\right ], \left [\frac {3}{2}, \frac {3}{2}\right ], -b^{2} x^{2}\right )}{\sqrt {\pi }}\) | \(23\) |
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\[ \int \frac {\text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )}{x} \,d x } \]
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Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {\text {erf}(b x)}{x} \, dx=\frac {2 b x {{}_{2}F_{2}\left (\begin {matrix} \frac {1}{2}, \frac {1}{2} \\ \frac {3}{2}, \frac {3}{2} \end {matrix}\middle | {- b^{2} x^{2}} \right )}}{\sqrt {\pi }} \]
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\[ \int \frac {\text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )}{x} \,d x } \]
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\[ \int \frac {\text {erf}(b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )}{x} \,d x } \]
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Timed out. \[ \int \frac {\text {erf}(b x)}{x} \, dx=\int \frac {\mathrm {erf}\left (b\,x\right )}{x} \,d x \]
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