Question

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

Answer 1

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

Let $1+e^x=t$

$e^{x}dx=dt$

Therefore,

$I=\int \frac{dt}{t}$

$I=\log t+C$

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