How to check whether the following limit exists and if it does how to solve it.
$\lim_{x \to \infty}~(\int_0^{x}\frac{t^2}{(1+t^3)^2}dt)$
I tried to solve it by directly replacing x with $\infty$ but I am getting nowhere. I just possess the basic knowledge of calculus and analysis so any help at my level will be appreciated.
You can calculate your integral by substituting $$1+t^3=u$$ then we get $$3t^2dt=du$$