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Antiderivative of cotangent

  • Thread starter mcmw
  • Start date
  • #1
5
0

Homework Statement


integral (t * csc^2 (t) ) dt


Homework Equations





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)
 

Answers and Replies

  • #2
G01
Homework Helper
Gold Member
2,665
16
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.
 
  • #3
529
1
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
529
1
  • #5
Gib Z
Homework Helper
3,346
5
[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]
 

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