Question

How to solve integral of cot pi*x

Answer 1

Start with a substitution:

`u = sin(\pi x) \\ du = \pi cos(\pi x) dx`
This will transform the integral into a function of "u"

`\int cot(\pi x) dx \\ = \int (cos(\pi x))/(sin(\pi x)) dx \\ = (1)/(\pi) \int (cos(\pi x))/(u) (du)/(cos(\pi x)) \\ =(1)/(\pi) \int (du)/(u) \\ .............\\ =(1)/(\pi) ln(u) +C \\............ \\ =(1)/(\pi) ln(sin(\pi x)) +C`