3.125 \(\int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\sin ^{-1}(a x)^{3/2} (b x)^m,x\right ) \]

[Out]

Unintegrable((b*x)^m*arcsin(a*x)^(3/2),x)

________________________________________________________________________________________

Rubi [A]  time = 0.02, 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 = {} \[ \int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(b*x)^m*ArcSin[a*x]^(3/2),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 2.69, size = 0, normalized size = 0.00 \[ \int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(b*x)^m*ArcSin[a*x]^(3/2),x]

[Out]

Integrate[(b*x)^m*ArcSin[a*x]^(3/2), x]

________________________________________________________________________________________

fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m*arcsin(a*x)^(3/2), x)

________________________________________________________________________________________

maple [A]  time = 0.11, size = 0, normalized size = 0.00 \[ \int \left (b x \right )^{m} \arcsin \left (a x \right )^{\frac {3}{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m*arcsin(a*x)^(3/2),x)

[Out]

int((b*x)^m*arcsin(a*x)^(3/2),x)

________________________________________________________________________________________

maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative e
xponent.

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int {\mathrm {asin}\left (a\,x\right )}^{3/2}\,{\left (b\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(asin(a*x)^(3/2)*(b*x)^m, x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (b x\right )^{m} \operatorname {asin}^{\frac {3}{2}}{\left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m*asin(a*x)**(3/2),x)

[Out]

Integral((b*x)**m*asin(a*x)**(3/2), x)

________________________________________________________________________________________