∫dx/(1+e^x)?

Question

Calculus Question

Answer 1

Evaluate the integral ∫dx/(1 + e^x).

First let's algebraically manipulate the expression to make it easier to integrate.

1/(1 + e^x) = (1 + e^x - e^x) / (1 + e^x) = 1 - e^x/(1 + e^x)

Now we can integrate

∫[1/(1 + e^x)] dx = ∫[1 - e^x/(1 + e^x)] dx

= x - ln(1 + e^x) + C

Answer 2

Use e^-x this time. -ln(1+e^-x) + c