Question

Evaluate $\int \frac{e^x}{(1+e^x)}dx=log(1+e^x)$.

Answer 1

Let $I=\int \frac{e^x}{(1+e^x)}dx$
Put $1+e^x=t$

$\Rightarrow e^{x}dx=dt$
Therefore
$I=\int \frac{dt}{t}$

$=\log t+C$

$I=\log (1+e^x)+C$