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

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (e^{c+d x^2} \text{Erfc}(a+b x),x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0141731, 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 = {} \[ \int e^{c+d x^2} \text{Erfc}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(c + d*x^2)*Erfc[a + b*x],x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.0446625, size = 0, normalized size = 0. \[ \int e^{c+d x^2} \text{Erfc}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.123, size = 0, normalized size = 0. \begin{align*} \int{{\rm e}^{d{x}^{2}+c}}{\it erfc} \left ( bx+a \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(c)*Integral(exp(d*x**2)*erfc(a + b*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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