\(\int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx\) [98]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\text {Int}\left (\frac {1}{x^2 \sqrt {\arcsin (a x)}},x\right ) \]

[Out]

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

[In]

Int[1/(x^2*Sqrt[ArcSin[a*x]]),x]

[Out]

Defer[Int][1/(x^2*Sqrt[ArcSin[a*x]]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 2.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx \]

[In]

Integrate[1/(x^2*Sqrt[ArcSin[a*x]]),x]

[Out]

Integrate[1/(x^2*Sqrt[ArcSin[a*x]]), x]

Maple [N/A] (verified)

Not integrable

Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

\[\int \frac {1}{x^{2} \sqrt {\arcsin \left (a x \right )}}d x\]

[In]

int(1/x^2/arcsin(a*x)^(1/2),x)

[Out]

int(1/x^2/arcsin(a*x)^(1/2),x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/x^2/arcsin(a*x)^(1/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

Sympy [N/A]

Not integrable

Time = 0.49 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\int \frac {1}{x^{2} \sqrt {\operatorname {asin}{\left (a x \right )}}}\, dx \]

[In]

integrate(1/x**2/asin(a*x)**(1/2),x)

[Out]

Integral(1/(x**2*sqrt(asin(a*x))), x)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate(1/x^2/arcsin(a*x)^(1/2),x, algorithm="maxima")

[Out]

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

Giac [N/A]

Not integrable

Time = 0.40 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\int { \frac {1}{x^{2} \sqrt {\arcsin \left (a x\right )}} \,d x } \]

[In]

integrate(1/x^2/arcsin(a*x)^(1/2),x, algorithm="giac")

[Out]

integrate(1/(x^2*sqrt(arcsin(a*x))), x)

Mupad [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \sqrt {\arcsin (a x)}} \, dx=\int \frac {1}{x^2\,\sqrt {\mathrm {asin}\left (a\,x\right )}} \,d x \]

[In]

int(1/(x^2*asin(a*x)^(1/2)),x)

[Out]

int(1/(x^2*asin(a*x)^(1/2)), x)