3.119 \(\int (b x)^m \sin ^{-1}(a x)^4 \, dx\)

Optimal. Leaf size=65 \[ \frac {\sin ^{-1}(a x)^4 (b x)^{m+1}}{b (m+1)}-\frac {4 a \text {Int}\left (\frac {\sin ^{-1}(a x)^3 (b x)^{m+1}}{\sqrt {1-a^2 x^2}},x\right )}{b (m+1)} \]

[Out]

(b*x)^(1+m)*arcsin(a*x)^4/b/(1+m)-4*a*Unintegrable((b*x)^(1+m)*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)/b/(1+m)

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Rubi [A]  time = 0.12, 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 = {} \[ \int (b x)^m \sin ^{-1}(a x)^4 \, dx \]

Verification is Not applicable to the result.

[In]

Int[(b*x)^m*ArcSin[a*x]^4,x]

[Out]

((b*x)^(1 + m)*ArcSin[a*x]^4)/(b*(1 + m)) - (4*a*Defer[Int][((b*x)^(1 + m)*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2], x
])/(b*(1 + m))

Rubi steps

\begin {align*} \int (b x)^m \sin ^{-1}(a x)^4 \, dx &=\frac {(b x)^{1+m} \sin ^{-1}(a x)^4}{b (1+m)}-\frac {(4 a) \int \frac {(b x)^{1+m} \sin ^{-1}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx}{b (1+m)}\\ \end {align*}

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Mathematica [A]  time = 1.06, size = 0, normalized size = 0.00 \[ \int (b x)^m \sin ^{-1}(a x)^4 \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(b*x)^m*ArcSin[a*x]^4,x]

[Out]

Integrate[(b*x)^m*ArcSin[a*x]^4, x]

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fricas [A]  time = 0.47, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (b x\right )^{m} \arcsin \left (a x\right )^{4}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m*arcsin(a*x)^4,x, algorithm="fricas")

[Out]

integral((b*x)^m*arcsin(a*x)^4, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (b x\right )^{m} \arcsin \left (a x\right )^{4}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m*arcsin(a*x)^4,x, algorithm="giac")

[Out]

integrate((b*x)^m*arcsin(a*x)^4, x)

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maple [A]  time = 1.17, size = 0, normalized size = 0.00 \[ \int \left (b x \right )^{m} \arcsin \left (a x \right )^{4}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m*arcsin(a*x)^4,x)

[Out]

int((b*x)^m*arcsin(a*x)^4,x)

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m*arcsin(a*x)^4,x, algorithm="maxima")

[Out]

Timed out

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mupad [A]  time = 0.00, size = -1, normalized size = -0.02 \[ \int {\mathrm {asin}\left (a\,x\right )}^4\,{\left (b\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(asin(a*x)^4*(b*x)^m,x)

[Out]

int(asin(a*x)^4*(b*x)^m, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (b x\right )^{m} \operatorname {asin}^{4}{\left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m*asin(a*x)**4,x)

[Out]

Integral((b*x)**m*asin(a*x)**4, x)

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