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

Optimal. Leaf size=23 \[ b^2 \text{CannotIntegrate}\left (\frac{e^{\sin ^{-1}(a+b x)^2}}{b^2 x^2},x\right ) \]

[Out]

b^2*CannotIntegrate[E^ArcSin[a + b*x]^2/(b^2*x^2), x]

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Rubi [A]  time = 0.263946, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{e^{\sin ^{-1}(a+b x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

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

Mathematica [A]  time = 0.461235, size = 0, normalized size = 0. \[ \int \frac{e^{\sin ^{-1}(a+b x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^ArcSin[a + b*x]^2/x^2,x]

[Out]

Integrate[E^ArcSin[a + b*x]^2/x^2, x]

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Maple [A]  time = 0.01, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{ \left ( \arcsin \left ( bx+a \right ) \right ) ^{2}}}}{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\operatorname{asin}^{2}{\left (a + b x \right )}}}{x^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\left (\arcsin \left (b x + a\right )^{2}\right )}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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