Question

Solve this integral ASAP??​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{dx}{1 - \cos(x) }$

$= \int \frac{dx}{1 - \frac{1 - \tan^{2} ( \frac{x}{2} ) }{1 + \tan^{2} ( \frac{x}{2} ) } }$

$= \int \frac{ \sec^{2} ( \frac{x}{2} ) dx}{2 \tan ^{2} ( \frac{x}{2} ) }$

$let \: \: \tan( \frac{x}{2} ) = y \\ \implies \frac{1}{2} \sec^{2} ( \frac{x}{2} ) dx = dy$

$= \int \frac{dy}{y^{2} }$

$= - \frac{1}{y} + c$

$= - \frac{1}{ \tan( \frac{x}{2} ) } + c$