\(\int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx\) [462]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=b^2 \text {Int}\left (\frac {e^{\arcsin (a+b x)^2}}{b^2 x^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.20 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx \]

[In]

Int[E^ArcSin[a + b*x]^2/x^2,x]

[Out]

b*Defer[Subst][Defer[Int][(E^x^2*Cos[x])/(a - Sin[x])^2, x], x, ArcSin[a + b*x]]

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

Mathematica [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx \]

[In]

Integrate[E^ArcSin[a + b*x]^2/x^2,x]

[Out]

Integrate[E^ArcSin[a + b*x]^2/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

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

[Out]

integral(e^(arcsin(b*x + a)^2)/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.47 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int \frac {e^{\operatorname {asin}^{2}{\left (a + b x \right )}}}{x^{2}}\, dx \]

[In]

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

[Out]

Integral(exp(asin(a + b*x)**2)/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.48 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(e^(arcsin(b*x + a)^2)/x^2, x)

Giac [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(e^(arcsin(b*x + a)^2)/x^2, x)

Mupad [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\arcsin (a+b x)^2}}{x^2} \, dx=\int \frac {{\mathrm {e}}^{{\mathrm {asin}\left (a+b\,x\right )}^2}}{x^2} \,d x \]

[In]

int(exp(asin(a + b*x)^2)/x^2,x)

[Out]

int(exp(asin(a + b*x)^2)/x^2, x)