Optimal. Leaf size=92 \[ b^2 \text{Unintegrable}\left (\frac{e^{b^2 x^2+c} \text{Erfi}(b x)}{x},x\right )-\frac{e^{b^2 x^2+c} \text{Erfi}(b x)}{2 x^2}+\sqrt{2} b^2 e^c \text{Erfi}\left (\sqrt{2} b x\right )-\frac{b e^{2 b^2 x^2+c}}{\sqrt{\pi } x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.111064, 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 = {} \[ \int \frac{e^{c+b^2 x^2} \text{Erfi}(b x)}{x^3} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^3} \, dx &=-\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*}
Mathematica [A] time = 0.146748, size = 0, normalized size = 0. \[ \int \frac{e^{c+b^2 x^2} \text{Erfi}(b x)}{x^3} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.263, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{{b}^{2}{x}^{2}+c}}{\it erfi} \left ( bx \right ) }{{x}^{3}}}\, 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\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}}\,{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\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}}, 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^{b^{2} x^{2}} \operatorname{erfi}{\left (b x \right )}}{x^{3}}\, 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\right ) e^{\left (b^{2} x^{2} + c\right )}}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]