Integrand size = 19, antiderivative size = 19 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=-\frac {e^{c+d x^2} \text {erfi}(a+b x)}{x}+\frac {2 b \text {Int}\left (\frac {e^{a^2+c+2 a b x+\left (b^2+d\right ) x^2}}{x},x\right )}{\sqrt {\pi }}+2 d \text {Int}\left (e^{c+d x^2} \text {erfi}(a+b x),x\right ) \]
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Not integrable
Time = 0.15 (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 = {} \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {e^{c+d x^2} \text {erfi}(a+b x)}{x}+(2 d) \int e^{c+d x^2} \text {erfi}(a+b x) \, dx+\frac {(2 b) \int \frac {e^{a^2+c+2 a b x+\left (b^2+d\right ) x^2}}{x} \, dx}{\sqrt {\pi }} \\ \end{align*}
Not integrable
Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.08 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95
\[\int \frac {{\mathrm e}^{d \,x^{2}+c} \operatorname {erfi}\left (b x +a \right )}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 6.16 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=e^{c} \int \frac {e^{d x^{2}} \operatorname {erfi}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 5.74 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx=\int \frac {\mathrm {erfi}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c}}{x^2} \,d x \]
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