\(\int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx\) [450]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=a^2 \text {Int}\left (\frac {e^{\arcsin (a x)^2}}{a^2 x^2},x\right ) \]

[Out]

a^2*CannotIntegrate(exp(arcsin(a*x)^2)/a^2/x^2,x)

Rubi [N/A]

Not integrable

Time = 0.06 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx \]

[In]

Int[E^ArcSin[a*x]^2/x^2,x]

[Out]

a*Defer[Subst][Defer[Int][E^x^2*Cot[x]*Csc[x], x], x, ArcSin[a*x]]

Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int a^2 e^{x^2} \cot (x) \csc (x) \, dx,x,\arcsin (a x)\right )}{a} \\ & = a \text {Subst}\left (\int e^{x^2} \cot (x) \csc (x) \, dx,x,\arcsin (a x)\right ) \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 1.47 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx \]

[In]

Integrate[E^ArcSin[a*x]^2/x^2,x]

[Out]

Integrate[E^ArcSin[a*x]^2/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

\[\int \frac {{\mathrm e}^{\arcsin \left (a x \right )^{2}}}{x^{2}}d x\]

[In]

int(exp(arcsin(a*x)^2)/x^2,x)

[Out]

int(exp(arcsin(a*x)^2)/x^2,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsin(a*x)^2)/x^2,x, algorithm="fricas")

[Out]

integral(e^(arcsin(a*x)^2)/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.38 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int \frac {e^{\operatorname {asin}^{2}{\left (a x \right )}}}{x^{2}}\, dx \]

[In]

integrate(exp(asin(a*x)**2)/x**2,x)

[Out]

Integral(exp(asin(a*x)**2)/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.42 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsin(a*x)^2)/x^2,x, algorithm="maxima")

[Out]

integrate(e^(arcsin(a*x)^2)/x^2, x)

Giac [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsin(a*x)^2)/x^2,x, algorithm="giac")

[Out]

integrate(e^(arcsin(a*x)^2)/x^2, x)

Mupad [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a x)^2}}{x^2} \, dx=\int \frac {{\mathrm {e}}^{{\mathrm {asin}\left (a\,x\right )}^2}}{x^2} \,d x \]

[In]

int(exp(asin(a*x)^2)/x^2,x)

[Out]

int(exp(asin(a*x)^2)/x^2, x)