\(\int \frac {\text {erf}(b x)^2}{x^2} \, dx\) [32]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\text {Int}\left (\frac {\text {erf}(b x)^2}{x^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int \frac {\text {erf}(b x)^2}{x^2} \, dx \]

[In]

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

[Out]

Defer[Int][Erf[b*x]^2/x^2, x]

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

Mathematica [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int \frac {\text {erf}(b x)^2}{x^2} \, dx \]

[In]

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

[Out]

Integrate[Erf[b*x]^2/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {erf}\left (b x \right )^{2}}{x^{2}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )^{2}}{x^{2}} \,d x } \]

[In]

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

[Out]

integral(erf(b*x)^2/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.95 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int \frac {\operatorname {erf}^{2}{\left (b x \right )}}{x^{2}}\, dx \]

[In]

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

[Out]

Integral(erf(b*x)**2/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 3.70 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )^{2}}{x^{2}} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int { \frac {\operatorname {erf}\left (b x\right )^{2}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(erf(b*x)^2/x^2, x)

Mupad [N/A]

Not integrable

Time = 5.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erf}(b x)^2}{x^2} \, dx=\int \frac {{\mathrm {erf}\left (b\,x\right )}^2}{x^2} \,d x \]

[In]

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

[Out]

int(erf(b*x)^2/x^2, x)