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

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x^2 \sin ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable(1/x^2/arcsin(a*x)^2,x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {1}{x^2 \sin ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcSin[a*x]^2),x]

[Out]

Defer[Int][1/(x^2*ArcSin[a*x]^2), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \sin ^{-1}(a x)^2} \, dx &=\int \frac {1}{x^2 \sin ^{-1}(a x)^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 9.01, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \sin ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcSin[a*x]^2),x]

[Out]

Integrate[1/(x^2*ArcSin[a*x]^2), x]

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fricas [A]  time = 0.77, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \arcsin \left (a x\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^2,x, algorithm="fricas")

[Out]

integral(1/(x^2*arcsin(a*x)^2), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arcsin \left (a x\right )^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^2,x, algorithm="giac")

[Out]

integrate(1/(x^2*arcsin(a*x)^2), x)

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maple [A]  time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arcsin \left (a x \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arcsin(a*x)^2,x)

[Out]

int(1/x^2/arcsin(a*x)^2,x)

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^2,x, algorithm="maxima")

[Out]

Timed out

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x^2\,{\mathrm {asin}\left (a\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*asin(a*x)^2),x)

[Out]

int(1/(x^2*asin(a*x)^2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \operatorname {asin}^{2}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/asin(a*x)**2,x)

[Out]

Integral(1/(x**2*asin(a*x)**2), x)

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