`int cos(x)/(sin^2(x)) dx` Evaluate the indefinite integral.

You need to use the following substitution `sin x = t,` such that:

`sin x= t => cos x dx = dt`

`int (cos x*dx)/(sin^2 x) = int (dt)/(t^2)`

`int (dt)/(t^2) = int t^(-2) dt`

Using the formula `int t^(n) dt = (t^(n+1))/(n+1) + c` , yields

`int t^(-2) dt = (t^(-2+1))/(-2+1) + c`

`int t^(-2) dt = -1/t + c`

Replacing back  `sin x` for `t` yields:

`int (cos x*dx)/(sin^2 x) =- 1/(sin x) + c`

Hence, evaluating the indefinite integral, yields `int (cos x*dx)/(sin^2 x) =- 1/(sin x) + c.`