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

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {(b x)^m}{\sin ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable((b*x)^m/arcsin(a*x)^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 = {} \[ \int \frac {(b x)^m}{\sin ^{-1}(a x)^2} \, dx \]

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 = 0.59, size = 0, normalized size = 0.00 \[ \int \frac {(b x)^m}{\sin ^{-1}(a x)^2} \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.53, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}}, x\right ) \]

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

maple [A]  time = 0.70, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x \right )^{m}}{\arcsin \left (a x \right )^{2}}\, dx \]

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)

________________________________________________________________________________________

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)^2,x, algorithm="maxima")

[Out]

Timed out

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\left (b\,x\right )}^m}{{\mathrm {asin}\left (a\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((b*x)^m/asin(a*x)^2, x)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________