Integral of Cot^2(x)

Question: 

$\int cot^2(x) dx$

Solution:

We can Use the identity , $cot^{2}(x) = cosec^{2}(x)-1$

We can rewrite the integral as follows,

$\int cot^{2}(x) = \int (cosec^{2}(x)-1)dx$

$= \int cosec^{2}(x)dx - \int 1.dx$                      [Recall, $\int cosec^{2}x = -cot(x)$]

= -cot(x) - x + C