Question

Integrate the function $\frac{x^2}{(2+3x^3{)}^3}$

Answer 1

Put $2+3x^3=t$
$\therefore 9x^{2}dx=dt$
$\Rightarrow \int \frac{x^2}{(2+3x^3{)}^3}dx=\frac{1}{9}\int \frac{dt}{(t{)}^3}$
$=\frac{1}{9}\left[\frac{t^{-2}}{-2}\right]+C$
$=\frac{-1}{18}\left(\frac{1}{t^2}\right)+C$
$=\frac{-1}{18(2+3x^3{)}^2}+C$