Core 4 Integration (by substitution... Hard) rep+

Hey guys!

I am really stuck on this, so some help would be much appreciated!

By using the substitution t=e^x, show that integral of e^2x/(1+e^x)= integral of t/(1+t).

Thats fine and I have done that, now it says....
Deduce that integral of e^2x/(1+e^x)= e^x-ln(1+e^x)+c

Now I dont know how to remove the denominator when dividing t by (1+t).

If I were to do it normally I WOULD do Tln(1+t)+c
which is e^x.ln (1+e^x)+c

I don't know how they got that answer above of e^x-ln(1+e^x)+c

Help please!!

t/( 1 + t ) is equivalent to ( 1 + t -1 )/( 1 + t ) or

1 - 1/( 1 + t )...

okay so how would I integrate (1 +t -1)/(1+t) ?
This is confusing me

okay so how would I integrate (1 +t -1)/(1+t) ?
This is confusing me