\(\int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx\) [128]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\text {Int}\left (\frac {(b x)^m}{\arcsin (a x)^{3/2}},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx \]

[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*} \text {integral}& = \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.63 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86

\[\int \frac {\left (b x \right )^{m}}{\arcsin \left (a x \right )^{\frac {3}{2}}}d x\]

[In]

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

[Out]

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

Fricas [F(-2)]

Exception generated. \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\text {Exception raised: TypeError} \]

[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)

Sympy [N/A]

Not integrable

Time = 3.79 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\int \frac {\left (b x\right )^{m}}{\operatorname {asin}^{\frac {3}{2}}{\left (a x \right )}}\, dx \]

[In]

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

[Out]

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

Maxima [F(-2)]

Exception generated. \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\text {Exception raised: RuntimeError} \]

[In]

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

[Out]

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negative exponent.

Giac [N/A]

Not integrable

Time = 0.97 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{\frac {3}{2}}} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {(b x)^m}{\arcsin (a x)^{3/2}} \, dx=\int \frac {{\left (b\,x\right )}^m}{{\mathrm {asin}\left (a\,x\right )}^{3/2}} \,d x \]

[In]

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

[Out]

int((b*x)^m/asin(a*x)^(3/2), x)