integrate (e^2x)/(e^2x + 3e^x + 2)
Put e^x =t
so e^xdx =dt
hence
$\displaystyle
dx=dt/t
$
$\displaystyle
\int{\frac{t^2dt}{(t^2+3t+2)t}}
$
$\displaystyle
=\int{\frac{tdt}{(t^2+3t+2)}}
$
$\displaystyle =\int{\frac{tdt}{(t^2+2t+t+2)}}$
$\displaystyle
=\int{\frac{tdt}{(t(t+2)+(t+2))}}
$
$\displaystyle
=\int{\frac{tdt}{(t+1)(t+2)}}
$
go ahead infact the factorisation is not required at this stage