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

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\text {erf}(b x)^2}{x^4},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\text {erf}(b x)^2}{x^4} \, dx \]

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]

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fricas [A]  time = 0.65, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {erf}\left (b x\right )^{2}}{x^{4}}, x\right ) \]

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)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erf}\left (b x\right )^{2}}{x^{4}}\,{d x} \]

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)

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maple [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int \frac {\erf \left (b x \right )^{2}}{x^{4}}\, dx \]

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)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {4 \, b \int \frac {\operatorname {erf}\left (b x\right ) e^{\left (-b^{2} x^{2}\right )}}{x^{3}}\,{d x}}{3 \, \sqrt {\pi }} - \frac {\operatorname {erf}\left (b x\right )^{2}}{3 \, x^{3}} \]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {{\mathrm {erf}\left (b\,x\right )}^2}{x^4} \,d x \]

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)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erf}^{2}{\left (b x \right )}}{x^{4}}\, dx \]

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)

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