3.461 \(\int \frac {e^{\sin ^{-1}(a+b x)^2}}{x} \, dx\)

Optimal. Leaf size=22 \[ b \text {Int}\left (\frac {e^{\sin ^{-1}(a+b x)^2}}{b x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.20, 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 = {} \[ \int \frac {e^{\sin ^{-1}(a+b x)^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^ArcSin[a + b*x]^2/x,x]

[Out]

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

Rubi steps

\begin {align*} \int \frac {e^{\sin ^{-1}(a+b x)^2}}{x} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {e^{x^2} \cos (x)}{-\frac {a}{b}+\frac {\sin (x)}{b}} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=\frac {\operatorname {Subst}\left (\int \frac {b e^{x^2} \cos (x)}{-a+\sin (x)} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=\operatorname {Subst}\left (\int \frac {e^{x^2} \cos (x)}{-a+\sin (x)} \, dx,x,\sin ^{-1}(a+b x)\right )\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.15, size = 0, normalized size = 0.00 \[ \int \frac {e^{\sin ^{-1}(a+b x)^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^ArcSin[a + b*x]^2/x,x]

[Out]

Integrate[E^ArcSin[a + b*x]^2/x, x]

________________________________________________________________________________________

fricas [A]  time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(e^(arcsin(b*x + a)^2)/x, x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(arcsin(b*x + a)^2)/x, x)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{\arcsin \left (b x +a \right )^{2}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(arcsin(b*x + a)^2)/x, x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {e}}^{{\mathrm {asin}\left (a+b\,x\right )}^2}}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(asin(a + b*x)^2)/x,x)

[Out]

int(exp(asin(a + b*x)^2)/x, x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(exp(asin(a + b*x)**2)/x, x)

________________________________________________________________________________________