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Homework Help: Trig substitution

  1. Feb 26, 2010 #1
    Hi Everyone!
    I just need some guidance on this problem. I seem to have trouble what integration technique I need to use on integrals of this type.


    1. The problem statement, all variables and given/known data

    integrate 1/(25-x^2)

    2. Relevant equations

    sqrt(a^2-u^2)
    arcsin(u/a)

    3. The attempt at a solution

    Would I be able to use trig substitution for this type of integral? It almost fits with the arcsin but the square root is missing.
     
  2. jcsd
  3. Feb 26, 2010 #2
    Try partial fractions since 25-x^2 = (5-x)^2.
     
  4. Feb 26, 2010 #3

    Mark44

    Staff: Mentor

    Partial fractions is the easiest way to go, but 25 - x^2 = (5 - x)(5 + x), which is not equal to (5 - x)^2.
     
  5. Feb 26, 2010 #4
    Ok, I believe I figured it out.

    I used trig substitution

    set x = 5sinx
    dx/dθ = 5cosx -> dx = 5cosx dθ

    I got this... int 1/(25-(5sinx)^2) 5cosx dθ which is easy to reduce.
     
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