Start with a substitution:
[tex]u = sin(\pi x) \\ du = \pi cos(\pi x) dx[/tex]
This will transform the integral into a function of "u"
[tex]\int cot(\pi x) dx \\ = \int \frac{cos(\pi x)}{sin(\pi x)} dx \\ = \frac{1}{\pi} \int \frac{cos(\pi x)}{u} \frac{du}{cos(\pi x)} \\ =\frac{1}{\pi} \int \frac{du}{u} \\ .............\\ =\frac{1}{\pi} ln(u) +C \\............ \\ =\frac{1}{\pi} ln(sin(\pi x)) +C[/tex]
