\(\int \frac {\arcsin (a x)^n}{x^2} \, dx\) [135]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\text {Int}\left (\frac {\arcsin (a x)^n}{x^2},x\right ) \]

[Out]

Unintegrable(arcsin(a*x)^n/x^2,x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int \frac {\arcsin (a x)^n}{x^2} \, dx \]

[In]

Int[ArcSin[a*x]^n/x^2,x]

[Out]

Defer[Int][ArcSin[a*x]^n/x^2, x]

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

Mathematica [N/A]

Not integrable

Time = 0.55 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int \frac {\arcsin (a x)^n}{x^2} \, dx \]

[In]

Integrate[ArcSin[a*x]^n/x^2,x]

[Out]

Integrate[ArcSin[a*x]^n/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int { \frac {\arcsin \left (a x\right )^{n}}{x^{2}} \,d x } \]

[In]

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

[Out]

integral(arcsin(a*x)^n/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.54 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int \frac {\operatorname {asin}^{n}{\left (a x \right )}}{x^{2}}\, dx \]

[In]

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

[Out]

Integral(asin(a*x)**n/x**2, x)

Maxima [F(-2)]

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

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int { \frac {\arcsin \left (a x\right )^{n}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(arcsin(a*x)^n/x^2, x)

Mupad [N/A]

Not integrable

Time = 0.08 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arcsin (a x)^n}{x^2} \, dx=\int \frac {{\mathrm {asin}\left (a\,x\right )}^n}{x^2} \,d x \]

[In]

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

[Out]

int(asin(a*x)^n/x^2, x)