Optimal. Leaf size=77 \[ \frac{2 b \text{Unintegrable}\left (\frac{e^{a^2+2 a b x+x^2 \left (b^2+d\right )+c}}{x},x\right )}{\sqrt{\pi }}+2 d \text{Unintegrable}\left (e^{c+d x^2} \text{Erfi}(a+b x),x\right )-\frac{e^{c+d x^2} \text{Erfi}(a+b x)}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.203134, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{e^{c+d x^2} \text{Erfi}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
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*}
Mathematica [A] time = 0.341624, size = 0, normalized size = 0. \[ \int \frac{e^{c+d x^2} \text{Erfi}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.131, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{d{x}^{2}+c}}{\it erfi} \left ( bx+a \right ) }{{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} e^{c} \int \frac{e^{d x^{2}} \operatorname{erfi}{\left (a + b x \right )}}{x^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]