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

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {x^m \sin ^{-1}(a x)^3}{\sqrt {1-a^2 x^2}},x\right ) \]

[Out]

Unintegrable(x^m*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)

________________________________________________________________________________________

Rubi [A]  time = 0.08, 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 = {} \[ \int \frac {x^m \sin ^{-1}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][(x^m*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2], x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.92, size = 0, normalized size = 0.00 \[ \int \frac {x^m \sin ^{-1}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-a^{2} x^{2} + 1} x^{m} \arcsin \left (a x\right )^{3}}{a^{2} x^{2} - 1}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)^3/(a^2*x^2 - 1), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \arcsin \left (a x\right )^{3}}{\sqrt {-a^{2} x^{2} + 1}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*arcsin(a*x)^3/sqrt(-a^2*x^2 + 1), x)

________________________________________________________________________________________

maple [A]  time = 0.70, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \arcsin \left (a x \right )^{3}}{\sqrt {-a^{2} x^{2}+1}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \arcsin \left (a x\right )^{3}}{\sqrt {-a^{2} x^{2} + 1}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*arcsin(a*x)^3/sqrt(-a^2*x^2 + 1), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m\,{\mathrm {asin}\left (a\,x\right )}^3}{\sqrt {1-a^2\,x^2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^m*asin(a*x)^3)/(1 - a^2*x^2)^(1/2),x)

[Out]

int((x^m*asin(a*x)^3)/(1 - a^2*x^2)^(1/2), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \operatorname {asin}^{3}{\left (a x \right )}}{\sqrt {- \left (a x - 1\right ) \left (a x + 1\right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x**m*asin(a*x)**3/sqrt(-(a*x - 1)*(a*x + 1)), x)

________________________________________________________________________________________