# Math Help - [SOLVED] partial fraction with e^x

1. ## [SOLVED] partial fraction with e^x

integrate (e^2x)/(e^2x + 3e^x + 2)

2. Originally Posted by twilightstr
integrate (e^2x)/(e^2x + 3e^x + 2)
Put e^x =t
so e^xdx =dt
hence
$
dx=dt/t
$

$
\int{\frac{t^2dt}{(t^2+3t+2)t}}
$

$
=\int{\frac{tdt}{(t^2+3t+2)}}

$

$=\int{\frac{tdt}{(t^2+2t+t+2)}}$

$
=\int{\frac{tdt}{(t(t+2)+(t+2))}}
$

$
=\int{\frac{tdt}{(t+1)(t+2)}}
$

go ahead infact the factorisation is not required at this stage

3. is the answer -lnle^x+1l + 2lnle^x+2l + c ?

4. Originally Posted by twilightstr
is the answer -lnle^x+1l + 2lnle^x+2l + c ?
yes

5. You can dispense the absolute value bars since those quantities are always positive.