(e^(3x)-2e^(2x)+(5e^x))/(e^x+1) how do I do this what is the techniques??

Answer 1

I'd start with a long division. The integrand then becomes

8 - 3e^x + e^(2x) - 8/(e^x+1)

8 - 8/(e^x+1) = e^x/(e^x+1)
if you let
u = e^x+1
du = e^x dx

and the integrand is now

-3e^x + e^(2x) - 8du/u
making the integral

-3e^x + 1/2 e^(2x) - 8log(e^x+1) + C