Find the integral: $\int \text{cosec } x (\text{cosec } x + \cot x) \, dx$
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-\cot x - \text{cosec } x + C$
We have
$\int\text{cosec } x (\text{cosec }x + \cot x) \, dx = \int \text{cosec }^2 x \, dx + \int \text{cosec }x \cot x \, dx$
$= -\cot x - \text{cosec }x + C$