3.124 \(\int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx\)

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{(b x)^m}{\sin ^{-1}(a x)^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0153909, 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 = {} \[ \int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][(b*x)^m/ArcSin[a*x]^2, x]

Rubi steps

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

Mathematica [A]  time = 0.575555, size = 0, normalized size = 0. \[ \int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[(b*x)^m/ArcSin[a*x]^2, x]

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Maple [A]  time = 0.434, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( bx \right ) ^{m}}{ \left ( \arcsin \left ( ax \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((b*x)^m/arcsin(a*x)^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b x\right )^{m}}{\operatorname{asin}^{2}{\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)**2,x)

[Out]

Integral((b*x)**m/asin(a*x)**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m/arcsin(a*x)^2, x)