Question

Integrate the function: $\frac {sin\ x}{1+ cos \ x}$

Answer 1

$Let\ 1 + cos \ x = t$
$∴ -sin \ x \ dx = dt$
$⇒ ∫\frac {sin\ x}{1+cos\ x} dx = ∫-\frac {dt}{t}$
$=$ $-log|t|+C$
$=$ $-log|1+cos\ x|+C$