1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Antiderivative of cotangent

  1. Mar 15, 2007 #1
    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. jcsd
  3. Mar 15, 2007 #2

    G01

    User Avatar
    Homework Helper
    Gold Member

    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.
     
  4. Mar 15, 2007 #3
    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)
     
  5. Mar 15, 2007 #4
  6. Mar 16, 2007 #5

    Gib Z

    User Avatar
    Homework Helper

    [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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Antiderivative of cotangent
  1. The Antiderivative (Replies: 7)

  2. Hard Antiderivative (Replies: 6)

  3. Tricky Antiderivative (Replies: 14)

Loading...