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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0226769, 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 = {} \[ \int \frac{\text{Erfc}(a+b x)^2}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Erfc[a + b*x]^2/(c + d*x),x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.557632, size = 0, normalized size = 0. \[ \int \frac{\text{Erfc}(a+b x)^2}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]  time = 0.365, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it erfc} \left ( bx+a \right ) \right ) ^{2}}{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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