Integrate cot2x

To integrate cot2x, also written as ∫cot2x dx, and cot 2x, we usually use a u substitution to build a new integration in terms of u, because the integral of cotu is a standard solution in formula books.

Let u=2x.

Then, du/dx=2.

We transpose for dx, to get an expression in terms of du.

We replace 2x with u, and dx with ½du to make a new integration in terms of u.

We move the constant ½ outside of the integral sign.

The integral of cotu is a standard solution in formula books, hence we can use that here.

Hence our solution becomes this.

We replace the u with 2x, and C is the integration constant.