\(\int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx\) [162]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\text {Int}\left (\frac {1}{x^2 (a+b \arcsin (c x))},x\right ) \]

[Out]

Unintegrable(1/x^2/(a+b*arcsin(c*x)),x)

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx \]

[In]

Int[1/(x^2*(a + b*ArcSin[c*x])),x]

[Out]

Defer[Int][1/(x^2*(a + b*ArcSin[c*x])), x]

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

Mathematica [N/A]

Not integrable

Time = 1.92 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx \]

[In]

Integrate[1/(x^2*(a + b*ArcSin[c*x])),x]

[Out]

Integrate[1/(x^2*(a + b*ArcSin[c*x])), x]

Maple [N/A] (verified)

Not integrable

Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.36 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (b \arcsin \left (c x\right ) + a\right )} x^{2}} \,d x } \]

[In]

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

[Out]

integral(1/(b*x^2*arcsin(c*x) + a*x^2), x)

Sympy [N/A]

Not integrable

Time = 0.59 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{x^{2} \left (a + b \operatorname {asin}{\left (c x \right )}\right )}\, dx \]

[In]

integrate(1/x**2/(a+b*asin(c*x)),x)

[Out]

Integral(1/(x**2*(a + b*asin(c*x))), x)

Maxima [N/A]

Not integrable

Time = 0.36 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (b \arcsin \left (c x\right ) + a\right )} x^{2}} \,d x } \]

[In]

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

[Out]

integrate(1/((b*arcsin(c*x) + a)*x^2), x)

Giac [N/A]

Not integrable

Time = 0.55 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (b \arcsin \left (c x\right ) + a\right )} x^{2}} \,d x } \]

[In]

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

[Out]

integrate(1/((b*arcsin(c*x) + a)*x^2), x)

Mupad [N/A]

Not integrable

Time = 0.11 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{x^2\,\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )} \,d x \]

[In]

int(1/(x^2*(a + b*asin(c*x))),x)

[Out]

int(1/(x^2*(a + b*asin(c*x))), x)