Question:
$\frac{x^{2}}{\left(2+3 x^{3}\right)^{3}}$
Solution:
Let $2+3 x^{3}=t$
$\therefore 9 x^{2} d x=d t$
$\Rightarrow \int \frac{x^{2}}{\left(2+3 x^{3}\right)^{3}} d x=\frac{1}{9} \int \frac{d t}{(t)^{3}}$
$=\frac{1}{9}\left[\frac{t^{-2}}{-2}\right]+\mathrm{C}$
$=\frac{-1}{18}\left(\frac{1}{t^{2}}\right)+\mathrm{C}$
$=\frac{-1}{18\left(2+3 x^{3}\right)^{2}}+\mathrm{C}$