3.33 \(\int \frac{\text{Erf}(b x)^2}{x^4} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{\text{Erf}(b x)^2}{x^4},x\right ) \]

[Out]

Unintegrable[Erf[b*x]^2/x^4, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0172838, 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 = {} \[ \int \frac{\text{Erf}(b x)^2}{x^4} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Erf[b*x]^2/x^4,x]

[Out]

Defer[Int][Erf[b*x]^2/x^4, x]

Rubi steps

\begin{align*} \int \frac{\text{erf}(b x)^2}{x^4} \, dx &=\int \frac{\text{erf}(b x)^2}{x^4} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0356966, size = 0, normalized size = 0. \[ \int \frac{\text{Erf}(b x)^2}{x^4} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Erf[b*x]^2/x^4,x]

[Out]

Integrate[Erf[b*x]^2/x^4, x]

________________________________________________________________________________________

Maple [A]  time = 0.051, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it Erf} \left ( bx \right ) \right ) ^{2}}{{x}^{4}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(erf(b*x)^2/x^4,x)

[Out]

int(erf(b*x)^2/x^4,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \frac{4 \, b \int \frac{\operatorname{erf}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x^{3}}\,{d x}}{3 \, \sqrt{\pi }} - \frac{\operatorname{erf}\left (b x\right )^{2}}{3 \, x^{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erf(b*x)^2/x^4,x, algorithm="maxima")

[Out]

4/3*b*integrate(erf(b*x)*e^(-b^2*x^2)/x^3, x)/sqrt(pi) - 1/3*erf(b*x)^2/x^3

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{erf}\left (b x\right )^{2}}{x^{4}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erf(b*x)^2/x^4,x, algorithm="fricas")

[Out]

integral(erf(b*x)^2/x^4, x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erf}^{2}{\left (b x \right )}}{x^{4}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erf(b*x)**2/x**4,x)

[Out]

Integral(erf(b*x)**2/x**4, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erf}\left (b x\right )^{2}}{x^{4}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(erf(b*x)^2/x^4,x, algorithm="giac")

[Out]

integrate(erf(b*x)^2/x^4, x)