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

Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}},x\right ) \]

[Out]

Unintegrable[(x^m*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2], x]

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Rubi [A]  time = 0.0953553, 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 = {} \[ \int \frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][(x^m*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2], x]

Rubi steps

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

Mathematica [A]  time = 0.862275, size = 0, normalized size = 0. \[ \int \frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.497, size = 0, normalized size = 0. \begin{align*} \int{{x}^{m} \left ( \arcsin \left ( ax \right ) \right ) ^{2}{\frac{1}{\sqrt{-{a}^{2}{x}^{2}+1}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*arcsin(a*x)^2/sqrt(-a^2*x^2 + 1), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)^2/(a^2*x^2 - 1), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*asin(a*x)**2/(-a**2*x**2+1)**(1/2),x)

[Out]

Integral(x**m*asin(a*x)**2/sqrt(-(a*x - 1)*(a*x + 1)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*arcsin(a*x)^2/sqrt(-a^2*x^2 + 1), x)