Question

How do you integrate `1/tan(x) dx`?

Answer 1

`int 1/tan x dx = ln abs(sin x) + C`

Explanation:

Note that:

`int 1/t dt = ln abs(t) + C`

So we find:

`int 1/tan x dx = int cos x/sin x dx`

`color(white)(int 1/tan x dx) = int (d/dx sin x)*1/sin x dx`

`color(white)(int 1/tan x dx) = ln abs(sin x) + C`

Answer 2

`int dx/tanx = int cosx/sinx dx = int (d(sinx))/sinx = ln abs (sinx)+ C`