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

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

[Out]

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

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Rubi [A]  time = 0.0897566, 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 = {} \[ \int \frac{x^m}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.384027, size = 0, normalized size = 0. \[ \int \frac{x^m}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.2, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}}{\arcsin \left ( ax \right ) }{\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)/(-a^2*x^2+1)^(1/2),x)

[Out]

int(x^m/arcsin(a*x)/(-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}}{\sqrt{-a^{2} x^{2} + 1} \arcsin \left (a x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), 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}}{{\left (a^{2} x^{2} - 1\right )} \arcsin \left (a x\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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