Integrand size = 19, antiderivative size = 19 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=-\frac {b e^{c+2 b^2 x^2}}{\sqrt {\pi } x}-\frac {e^{c+b^2 x^2} \text {erfi}(b x)}{2 x^2}+\sqrt {2} b^2 e^c \text {erfi}\left (\sqrt {2} b x\right )+b^2 \text {Int}\left (\frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {e^{c+b^2 x^2} \text {erfi}(b x)}{2 x^2}+b^2 \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x} \, dx+\frac {b \int \frac {e^{c+2 b^2 x^2}}{x^2} \, dx}{\sqrt {\pi }} \\ & = -\frac {b e^{c+2 b^2 x^2}}{\sqrt {\pi } x}-\frac {e^{c+b^2 x^2} \text {erfi}(b x)}{2 x^2}+b^2 \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x} \, dx+\frac {\left (4 b^3\right ) \int e^{c+2 b^2 x^2} \, dx}{\sqrt {\pi }} \\ & = -\frac {b e^{c+2 b^2 x^2}}{\sqrt {\pi } x}-\frac {e^{c+b^2 x^2} \text {erfi}(b x)}{2 x^2}+\sqrt {2} b^2 e^c \text {erfi}\left (\sqrt {2} b x\right )+b^2 \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.12 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95
\[\int \frac {{\mathrm e}^{b^{2} x^{2}+c} \operatorname {erfi}\left (b x \right )}{x^{3}}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}} \,d x } \]
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Not integrable
Time = 3.95 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=e^{c} \int \frac {e^{b^{2} x^{2}} \operatorname {erfi}{\left (b x \right )}}{x^{3}}\, dx \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}} \,d x } \]
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Not integrable
Time = 5.65 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+b^2 x^2} \text {erfi}(b x)}{x^3} \, dx=\int \frac {{\mathrm {e}}^{b^2\,x^2+c}\,\mathrm {erfi}\left (b\,x\right )}{x^3} \,d x \]
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