How to integrate cosec 2x

Remember that - csc^2 (x) is a known derivative; it is the derivative of cot (x).

Keeping that in mind, let's put a negative there, and then offset it with another negative, which can conveniently be placed outside of the integral.

(-1) Integral (-csc^2 (x) dx)

Which evaluates to

(-1) cot (x) + C

-cot (x) + C