\(\int \frac {(b x)^m}{\arcsin (a x)} \, dx\) [123]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\text {Int}\left (\frac {(b x)^m}{\arcsin (a x)},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int \frac {(b x)^m}{\arcsin (a x)} \, dx \]

[In]

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

[Out]

Defer[Int][(b*x)^m/ArcSin[a*x], x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {(b x)^m}{\arcsin (a x)} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int \frac {(b x)^m}{\arcsin (a x)} \, dx \]

[In]

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

[Out]

Integrate[(b*x)^m/ArcSin[a*x], x]

Maple [N/A] (verified)

Not integrable

Time = 0.32 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

\[\int \frac {\left (b x \right )^{m}}{\arcsin \left (a x \right )}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integral((b*x)^m/arcsin(a*x), x)

Sympy [N/A]

Not integrable

Time = 0.40 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int \frac {\left (b x\right )^{m}}{\operatorname {asin}{\left (a x \right )}}\, dx \]

[In]

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

[Out]

Integral((b*x)**m/asin(a*x), x)

Maxima [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integrate((b*x)^m/arcsin(a*x), x)

Giac [N/A]

Not integrable

Time = 0.43 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integrate((b*x)^m/arcsin(a*x), x)

Mupad [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)} \, dx=\int \frac {{\left (b\,x\right )}^m}{\mathrm {asin}\left (a\,x\right )} \,d x \]

[In]

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

[Out]

int((b*x)^m/asin(a*x), x)