Optimal. Leaf size=79 \[ \frac {2 b \text {Int}\left (\frac {e^{a^2+2 a b x+x^2 \left (b^2+d\right )+c}}{x},x\right )}{\sqrt {\pi }}+2 d \text {Int}\left (e^{c+d x^2} \text {erfi}(a+b x),x\right )-\frac {e^{c+d x^2} \text {erfi}(a+b x)}{x} \]
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Rubi [A] time = 0.20, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^{c+d x^2} \text {Erfi}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \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}+(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*}
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Mathematica [A] time = 0.40, size = 0, normalized size = 0.00 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{d \,x^{2}+c} \erfi \left (b x +a \right )}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {\mathrm {erfi}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c}}{x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ e^{c} \int \frac {e^{d x^{2}} \operatorname {erfi}{\left (a + b x \right )}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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