3.4.2 \(\int \frac {x^m \text {ArcSin}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx\) [302]

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

[Out]

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

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Rubi [A]
time = 0.06, 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 = {} \begin {gather*} \int \frac {x^m \text {ArcSin}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.60, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^m \text {ArcSin}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx \end {gather*}

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]

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Maple [A]
time = 0.30, 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)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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

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)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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

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)

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