\(\int \frac {\text {erfi}(b x)^2}{x^4} \, dx\) [239]

   Optimal result
   Rubi [N/A]
   Mathematica [N/A]
   Maple [N/A] (verified)
   Fricas [N/A]
   Sympy [N/A]
   Maxima [N/A]
   Giac [N/A]
   Mupad [N/A]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\text {Int}\left (\frac {\text {erfi}(b x)^2}{x^4},x\right ) \]

[Out]

Unintegrable(erfi(b*x)^2/x^4,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 = {} \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int \frac {\text {erfi}(b x)^2}{x^4} \, dx \]

[In]

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

[Out]

Defer[Int][Erfi[b*x]^2/x^4, x]

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

Mathematica [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int \frac {\text {erfi}(b x)^2}{x^4} \, dx \]

[In]

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

[Out]

Integrate[Erfi[b*x]^2/x^4, x]

Maple [N/A] (verified)

Not integrable

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {erfi}\left (b x \right )^{2}}{x^{4}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right )^{2}}{x^{4}} \,d x } \]

[In]

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

[Out]

integral(erfi(b*x)^2/x^4, x)

Sympy [N/A]

Not integrable

Time = 1.14 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int \frac {\operatorname {erfi}^{2}{\left (b x \right )}}{x^{4}}\, dx \]

[In]

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

[Out]

Integral(erfi(b*x)**2/x**4, x)

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right )^{2}}{x^{4}} \,d x } \]

[In]

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

[Out]

integrate(erfi(b*x)^2/x^4, x)

Giac [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int { \frac {\operatorname {erfi}\left (b x\right )^{2}}{x^{4}} \,d x } \]

[In]

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

[Out]

integrate(erfi(b*x)^2/x^4, x)

Mupad [N/A]

Not integrable

Time = 4.89 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {erfi}(b x)^2}{x^4} \, dx=\int \frac {{\mathrm {erfi}\left (b\,x\right )}^2}{x^4} \,d x \]

[In]

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

[Out]

int(erfi(b*x)^2/x^4, x)