Question

Integrate e^x/(1+e^(2x)) using substitution?

Answer 1

looks like
\[\int\frac{u}{1+u^2}du\]

Answer 2

Ahh, that was pretty easy! Been at this a little too long I think. Thanks!

Answer 3

anti derivative is
\[\frac{1}{2}\ln(u^2+1)\]

Answer 4

i mean you still have to make the substitution yes?

Answer 5

well, yeah, but I was having a hard time figuring out the form. From there it would be inverse tan(e^x)+C, correct?

Answer 6

wait wait

Answer 7

i steered you wrong. you have it. right exactly

Answer 8

\[u=e^x\] etc. you get
\[\tan^{-1}(u)=\tan^{-1}(e^x)\]

Answer 9

Thanks for the help!

Answer 10

latex all messed up

Answer 11

yw