\(\int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx\) [139]

Optimal result

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

[Out]

Unintegrable(arcsin(a*x)^n/(b*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 = {} \[ \int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx=\int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx \]

[In]

Int[ArcSin[a*x]^n/(b*x)^(3/2),x]

[Out]

Defer[Int][ArcSin[a*x]^n/(b*x)^(3/2), x]

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

Mathematica [N/A]

Not integrable

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

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43 \[ \int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx=\int { \frac {\arcsin \left (a x\right )^{n}}{\left (b x\right )^{\frac {3}{2}}} \,d x } \]

[In]

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

[Out]

integral(sqrt(b*x)*arcsin(a*x)^n/(b^2*x^2), x)

Sympy [N/A]

Not integrable

Time = 12.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx=\int \frac {\operatorname {asin}^{n}{\left (a x \right )}}{\left (b x\right )^{\frac {3}{2}}}\, dx \]

[In]

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

[Out]

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

Maxima [F(-2)]

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

[In]

integrate(arcsin(a*x)^n/(b*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 = 0.48 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx=\int { \frac {\arcsin \left (a x\right )^{n}}{\left (b x\right )^{\frac {3}{2}}} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {\arcsin (a x)^n}{(b x)^{3/2}} \, dx=\int \frac {{\mathrm {asin}\left (a\,x\right )}^n}{{\left (b\,x\right )}^{3/2}} \,d x \]

[In]

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

[Out]

int(asin(a*x)^n/(b*x)^(3/2), x)