Integrate cotx

To integrate cotx, also written as ∫cotx dx, we start with a commonly used trig manipulation so that we can change the form to one that allows us the use of u substitution.

We recall this well-known trig identity.

As you can see, we can rewrite our original integration problem in a different form that means the same thing and is easier to solve. We recall that if the differential of the denominator looks like the numerator, there is a good chance that u substitution would work.

Let u=sinx

Then du/dx = cosx.

We rearrange for du.

We can now replace cosx dx with du, and sinx with u, to give a new integration expression in terms of u. As you can see, they mean the same thing but the RHS is easier to solve.

We can now integrate 1/u, by looking up the integral for it in formula books. This is a standard solution usually found in most formula books. As you can see the answer will be ln|u|.

We can now replace u with sinx, and C is the integration constant.