Question

Evaluate :

$\int \frac{e^x}{e^x+1}dx$

Answer 1

$I=\int \frac{e^x}{e^x+1}dx$

Let $e^x+1=t$

Differentiating w.r.t. x, we get,

$e^{x}dx=dt$

$\therefore I=\int \frac{dt}{t}=\log t+C$

$I=\log |e^x+1|+C$