Antiderivative of cotangent

Integration by parts is the way I'd also go about this.

Hint: In terms of other trig functions, what is cotangent equal to? You should end up with something that is solvable by substitution.

 

The integral contains singularities whenever sin(x)=0, or x=n PI

If it's an integral over -T, to T then the integral is zero (by symmetry)

 

Well, the Integrator gives an answer.
http://integrals.wolfram.com/index.jsp

The integral of cot(x)=log(sin(x))

(yes, I know I'm cheating!)

 

[tex]\cot x = \frac{\cos x}{\sin x}[/tex]

[tex]\int \cot x dx = \int \frac{\cos x}{\sin x} dx[/tex].

let u= sin x, then du = cos x dx

[tex]\int \frac{1}{u} du = \ln u + C = \ln (\sin x) + C[/tex]