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

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {e^{-b^2 x^2} \text {erfc}(b x)}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {e^{-b^2 x^2} \text {Erfc}(b x)}{x} \, dx \]

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*}

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Mathematica [A]  time = 0.17, size = 0, normalized size = 0.00 \[ \int \frac {e^{-b^2 x^2} \text {erfc}(b x)}{x} \, dx \]

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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fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {{\left (\operatorname {erf}\left (b x\right ) - 1\right )} e^{\left (-b^{2} x^{2}\right )}}{x}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfc}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x}\,{d x} \]

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)

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maple [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {erfc}\left (b x \right ) {\mathrm e}^{-b^{2} x^{2}}}{x}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfc}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {e}}^{-b^2\,x^2}\,\mathrm {erfc}\left (b\,x\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((exp(-b^2*x^2)*erfc(b*x))/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{- b^{2} x^{2}} \operatorname {erfc}{\left (b x \right )}}{x}\, dx \]

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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