3.181 \(\int \frac{e^{-b^2 x^2} \text{Erfc}(b x)}{x} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{e^{-b^2 x^2} \text{Erfc}(b x)}{x},x\right ) \]

[Out]

Unintegrable[Erfc[b*x]/(E^(b^2*x^2)*x), x]

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Rubi [A]  time = 0.0324618, 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 = {} \[ \int \frac{e^{-b^2 x^2} \text{Erfc}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Erfc[b*x]/(E^(b^2*x^2)*x),x]

[Out]

Defer[Int][Erfc[b*x]/(E^(b^2*x^2)*x), x]

Rubi steps

\begin{align*} \int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x} \, dx &=\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.193638, size = 0, normalized size = 0. \[ \int \frac{e^{-b^2 x^2} \text{Erfc}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Erfc[b*x]/(E^(b^2*x^2)*x),x]

[Out]

Integrate[Erfc[b*x]/(E^(b^2*x^2)*x), x]

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Maple [A]  time = 0.133, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it erfc} \left ( bx \right ) }{{{\rm e}^{{b}^{2}{x}^{2}}}x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(erfc(b*x)/exp(b^2*x^2)/x,x)

[Out]

int(erfc(b*x)/exp(b^2*x^2)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)/exp(b^2*x^2)/x,x, algorithm="maxima")

[Out]

integrate(erfc(b*x)*e^(-b^2*x^2)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{{\left (\operatorname{erf}\left (b x\right ) - 1\right )} e^{\left (-b^{2} x^{2}\right )}}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)/exp(b^2*x^2)/x,x, algorithm="fricas")

[Out]

integral(-(erf(b*x) - 1)*e^(-b^2*x^2)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{- b^{2} x^{2}} \operatorname{erfc}{\left (b x \right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)/exp(b**2*x**2)/x,x)

[Out]

Integral(exp(-b**2*x**2)*erfc(b*x)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)/exp(b^2*x^2)/x,x, algorithm="giac")

[Out]

integrate(erfc(b*x)*e^(-b^2*x^2)/x, x)