# Antiderivative of cotangent

1. Mar 15, 2007

### mcmw

1. The problem statement, all variables and given/known data
integral (t * csc^2 (t) ) dt

2. Relevant equations

3. The attempt at a solution

t * -cot (t) - integral( 1 * -cot (t)) u= t dv= csc^2(t)
du= 1 v= - cot (t)
-t * cot(t) - ??? I don't understand how to find the antiderivative of -cot(t)

2. Mar 15, 2007

### G01

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

3. Mar 15, 2007

### christianjb

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)

4. Mar 15, 2007

### christianjb

5. Mar 16, 2007

### Gib Z

$$\cot x = \frac{\cos x}{\sin x}$$

$$\int \cot x dx = \int \frac{\cos x}{\sin x} dx$$.

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

$$\int \frac{1}{u} du = \ln u + C = \ln (\sin x) + C$$