3.66 \(\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sin ^{-1}(a x)^3},x\right ) \]

[Out]

Unintegrable[1/(x^2*ArcSin[a*x]^3), x]

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Rubi [A]  time = 0.0133543, 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 = {} \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcSin[a*x]^3),x]

[Out]

Defer[Int][1/(x^2*ArcSin[a*x]^3), x]

Rubi steps

\begin{align*} \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx &=\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx\\ \end{align*}

Mathematica [A]  time = 6.43086, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcSin[a*x]^3),x]

[Out]

Integrate[1/(x^2*ArcSin[a*x]^3), x]

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Maple [A]  time = 0.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2} \left ( \arcsin \left ( ax \right ) \right ) ^{3}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arcsin(a*x)^3,x)

[Out]

int(1/x^2/arcsin(a*x)^3,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{x^{3} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{2} \int \frac{a^{2} x^{2} - 6}{x^{4} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}\,{d x} + \sqrt{a x + 1} \sqrt{-a x + 1} a x +{\left (a^{2} x^{2} - 2\right )} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}{2 \, a^{2} x^{3} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^3,x, algorithm="maxima")

[Out]

-1/2*(x^3*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^2*integrate((a^2*x^2 - 6)/(x^4*arctan2(a*x, sqrt(a*x + 1)
*sqrt(-a*x + 1))), x) + sqrt(a*x + 1)*sqrt(-a*x + 1)*a*x + (a^2*x^2 - 2)*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x
+ 1)))/(a^2*x^3*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^2)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x^{2} \arcsin \left (a x\right )^{3}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^3,x, algorithm="fricas")

[Out]

integral(1/(x^2*arcsin(a*x)^3), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \operatorname{asin}^{3}{\left (a x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/asin(a*x)**3,x)

[Out]

Integral(1/(x**2*asin(a*x)**3), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \arcsin \left (a x\right )^{3}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^3,x, algorithm="giac")

[Out]

integrate(1/(x^2*arcsin(a*x)^3), x)