calculus. How to integrate?

Question

Evaluate  definite integral. The boundary is from 0 to ln(8). 

 

∫ (e^x)/(1+e^2x) dx

 

 

Answer 1

Let u = e^x so du = e^xdx and 1+e^2x = 1+u²

 

Now substitute and the antidifferentiation becomes easy.

 

don't forget to switch back to x language after the antidifferentiation so that you can use FTC with the limits 0 and ln 8.