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

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

[Out]

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

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Rubi [A]  time = 0.08, 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 = {} \[ \int \frac {e^{\sin ^{-1}(a x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

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

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Mathematica [A]  time = 1.83, size = 0, normalized size = 0.00 \[ \int \frac {e^{\sin ^{-1}(a x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[E^ArcSin[a*x]^2/x^2, x]

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fricas [A]  time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(e^(arcsin(a*x)^2)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(arcsin(a*x)^2)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^(arcsin(a*x)^2)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(exp(asin(a*x)^2)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(exp(asin(a*x)**2)/x**2, x)

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