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

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

[Out]

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

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Rubi [A]
time = 0.05, 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 = {} \begin {gather*} \int \frac {e^{\text {ArcSin}(a x)^2}}{x^2} \, dx \end {gather*}

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 {\text {Subst}\left (\int a^2 e^{x^2} \cot (x) \csc (x) \, dx,x,\sin ^{-1}(a x)\right )}{a}\\ &=a \text {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 = 1.23, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\text {ArcSin}(a x)^2}}{x^2} \, dx \end {gather*}

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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Maple [A]
time = 0.00, 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 \begin {gather*} \text {Failed to integrate} \end {gather*}

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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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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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