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Homework Help: Integral Calculus - Trigonometric Substitution

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data
    2
    ∫ dx / (x+1)√[2x(x+2)]
    1

    2. Relevant equations

    Let x = tan θ if √(a^2 + x^2)
    Where a = constant

    3. The attempt at a solution

    2
    ∫ dx / (x+1)√(2x)√(x+2)
    1

    2
    1/√2 ( ∫ dx / (√x)(x+1)[√(x+2)]
    1

    Now make all x in terms of √x so we can apply relevant equation ( applied also to constant )

    2
    1/√2 ( ∫ dx / (√x)((√x)^2+1)[√(√x+2)]
    1

    Now before i go on I want to ask if this is possible so I can apply the rule of the tangent in substitution?
     
  2. jcsd
  3. Jan 5, 2012 #2

    lanedance

    User Avatar
    Homework Helper

    how about noticing that
    [tex] 2x(x+2) = 2(x^2+2x) =2(x^2+2x+1-1) = 2((x+1)^2-1) [/tex]
     
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