What is the indefinite integral of f(x)=e^x/(e^2x +1)?

We'll solve the integral using substitution
technique.

Let e^x = t => e^x dx =
dt

`int` e^x dx/(e^2x +1) = `int` dt/(t^2 + 1) = arctan t +
C

`int` e^x dx/(e^2x +1) = arctan e^x +
C

The requested result of the indefinite
integral is represented by the primitive function F(x) = arctan e^x + C, where C
represents the family of constants.