What is the antiderivative of e^2/1+e^2?

Answer 1

well the term you've quoted is a constant...

so (e^2/1+e^2)x would be the answer to that question.

but i'm guessing you typed it wrong, or are confused.

Answer 2

You want to find:

Integral ( e^x / (1 + e^x) )dx

(I'm presuming you made an error because I know how typical questions look like)

In this case, you use substitution.

Let u = 1 + e^x
Then du = e^x dx

So our new question becomes:

Integral (1/u) du

Which is now an easy integral. It's
ln|u| + C

Substituting u=1+e^x back, we get
ln|1 + e^x| + C

Answer 3

I would'nt dare add to Puggy's exceptional answer to this question, except say that if you had any boundary/initial conditions, maybe that would help in the determination of the constant C in Puggy's exposition.....