3.137 \(\int \frac{\text{Erfc}(b x)^2}{x^6} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{\text{Erfc}(b x)^2}{x^6},x\right ) \]

[Out]

Unintegrable[Erfc[b*x]^2/x^6, x]

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Rubi [A]  time = 0.0168902, 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 = {} \[ \int \frac{\text{Erfc}(b x)^2}{x^6} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Erfc[b*x]^2/x^6,x]

[Out]

Defer[Int][Erfc[b*x]^2/x^6, x]

Rubi steps

\begin{align*} \int \frac{\text{erfc}(b x)^2}{x^6} \, dx &=\int \frac{\text{erfc}(b x)^2}{x^6} \, dx\\ \end{align*}

Mathematica [A]  time = 0.155884, size = 0, normalized size = 0. \[ \int \frac{\text{Erfc}(b x)^2}{x^6} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Erfc[b*x]^2/x^6,x]

[Out]

Integrate[Erfc[b*x]^2/x^6, x]

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Maple [A]  time = 0.059, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it erfc} \left ( bx \right ) \right ) ^{2}}{{x}^{6}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(erfc(b*x)^2/x^6,x)

[Out]

int(erfc(b*x)^2/x^6,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x\right )^{2}}{x^{6}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)^2/x^6,x, algorithm="maxima")

[Out]

integrate(erfc(b*x)^2/x^6, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{erf}\left (b x\right )^{2} - 2 \, \operatorname{erf}\left (b x\right ) + 1}{x^{6}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)^2/x^6,x, algorithm="fricas")

[Out]

integral((erf(b*x)^2 - 2*erf(b*x) + 1)/x^6, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}^{2}{\left (b x \right )}}{x^{6}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)**2/x**6,x)

[Out]

Integral(erfc(b*x)**2/x**6, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x\right )^{2}}{x^{6}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erfc(b*x)^2/x^6,x, algorithm="giac")

[Out]

integrate(erfc(b*x)^2/x^6, x)