How to find the integral of $\lim_ \ x^2 \arcsin(x^3)/\sqrt{1-x^6}\ dx$? I could really use some help trying to find this integral please.
$$\int \frac{x^2\arcsin(x^3)}{\sqrt{1-x^6}} dx$$

Based on the fact that if $\;f\;$ is a differential function, we have that
$$\int\frac{\arcsin x}{\sqrt{1-x^2}}dx=\frac{\arcsin^2 x}2+C\implies \int\frac{f'(x)\arcsin f(x)}{\sqrt{1-f(x)^2}}dx=\frac{\arcsin^2f(x)}2+C $$
solve your problem now with $\;f(x)=x^3\;$ 
