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

Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\sqrt{\sin ^{-1}(a x)} (b x)^m,x\right ) \]

[Out]

Unintegrable[(b*x)^m*Sqrt[ArcSin[a*x]], x]

________________________________________________________________________________________

Rubi [A]  time = 0.0152887, 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 = {} \[ \int (b x)^m \sqrt{\sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 2.9291, size = 0, normalized size = 0. \[ \int (b x)^m \sqrt{\sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]  time = 0.062, size = 0, normalized size = 0. \begin{align*} \int \left ( bx \right ) ^{m}\sqrt{\arcsin \left ( ax \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m*arcsin(a*x)^(1/2),x)

[Out]

int((b*x)^m*arcsin(a*x)^(1/2),x)

________________________________________________________________________________________

Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError

________________________________________________________________________________________

Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral((b*x)**m*sqrt(asin(a*x)), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m*sqrt(arcsin(a*x)), x)