3.159 \(\int \frac{e^{c+d x^2} \text{Erfc}(b x)}{x} \, dx\)

Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{\text{Erfc}(b x) e^{c+d x^2}}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0373325, 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 = {} \[ \int \frac{e^{c+d x^2} \text{Erfc}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(E^(c + d*x^2)*Erfc[b*x])/x,x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.487532, size = 0, normalized size = 0. \[ \int \frac{e^{c+d x^2} \text{Erfc}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.13, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{d{x}^{2}+c}}{\it erfc} \left ( bx \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(exp(d*x^2+c)*erfc(b*x)/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 (d x^{2} + c\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfc(b*x)*e^(d*x^2 + c)/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 (d x^{2} + c\right )}}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(d*x**2+c)*erfc(b*x)/x,x)

[Out]

exp(c)*Integral(exp(d*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 (d x^{2} + c\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfc(b*x)*e^(d*x^2 + c)/x, x)