Optimal. Leaf size=143 \[ \frac{4}{3} d^2 \text{Unintegrable}\left (\text{Erfi}(b x) e^{c+d x^2},x\right )+\frac{2 b e^c d \text{ExpIntegralEi}\left (x^2 \left (b^2+d\right )\right )}{3 \sqrt{\pi }}+\frac{b e^c \left (b^2+d\right ) \text{ExpIntegralEi}\left (x^2 \left (b^2+d\right )\right )}{3 \sqrt{\pi }}-\frac{b e^{x^2 \left (b^2+d\right )+c}}{3 \sqrt{\pi } x^2}-\frac{2 d \text{Erfi}(b x) e^{c+d x^2}}{3 x}-\frac{\text{Erfi}(b x) e^{c+d x^2}}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.272621, 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 = {} \[ \int \frac{e^{c+d x^2} \text{Erfi}(b x)}{x^4} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^4} \, dx &=-\frac{e^{c+d x^2} \text{erfi}(b x)}{3 x^3}+\frac{1}{3} (2 d) \int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^2} \, dx+\frac{(2 b) \int \frac{e^{c+\left (b^2+d\right ) x^2}}{x^3} \, dx}{3 \sqrt{\pi }}\\ &=-\frac{b e^{c+\left (b^2+d\right ) x^2}}{3 \sqrt{\pi } x^2}-\frac{e^{c+d x^2} \text{erfi}(b x)}{3 x^3}-\frac{2 d e^{c+d x^2} \text{erfi}(b x)}{3 x}+\frac{1}{3} \left (4 d^2\right ) \int e^{c+d x^2} \text{erfi}(b x) \, dx+\frac{(4 b d) \int \frac{e^{c+\left (b^2+d\right ) x^2}}{x} \, dx}{3 \sqrt{\pi }}+\frac{\left (2 b \left (b^2+d\right )\right ) \int \frac{e^{c+\left (b^2+d\right ) x^2}}{x} \, dx}{3 \sqrt{\pi }}\\ &=-\frac{b e^{c+\left (b^2+d\right ) x^2}}{3 \sqrt{\pi } x^2}-\frac{e^{c+d x^2} \text{erfi}(b x)}{3 x^3}-\frac{2 d e^{c+d x^2} \text{erfi}(b x)}{3 x}+\frac{2 b d e^c \text{Ei}\left (\left (b^2+d\right ) x^2\right )}{3 \sqrt{\pi }}+\frac{b \left (b^2+d\right ) e^c \text{Ei}\left (\left (b^2+d\right ) x^2\right )}{3 \sqrt{\pi }}+\frac{1}{3} \left (4 d^2\right ) \int e^{c+d x^2} \text{erfi}(b x) \, dx\\ \end{align*}
Mathematica [A] time = 0.291054, size = 0, normalized size = 0. \[ \int \frac{e^{c+d x^2} \text{Erfi}(b x)}{x^4} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.286, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{d{x}^{2}+c}}{\it erfi} \left ( bx \right ) }{{x}^{4}}}\, 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 (d x^{2} + c\right )}}{x^{4}}\,{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 (d x^{2} + c\right )}}{x^{4}}, 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 (b x \right )}}{x^{4}}\, 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 (d x^{2} + c\right )}}{x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]