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Homework Help: Trig substitution ∫(4x^3)/√(x^2+4)

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫(4x^3)/√(x^2+4)dx

    2. Relevant equations



    3. The attempt at a solution

    So, I let x= 2tanθ
    dx= 2sec^2θ dθ
    So, √(4tan^2(θ)+4)=2secθ
    ∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ.

    Would it go to ∫16tan^3(θ)2sec(θ)dθ
    or ∫32tan^3(θ)sec(θ)dθ
     
  2. jcsd
  3. Sep 10, 2012 #2

    ehild

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    Homework Helper

    It is correct so far.

    ehild
     
  4. Sep 10, 2012 #3

    Dick

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    Science Advisor
    Homework Helper

    I don't think you really need a trig substitution here. Try u=x^2+4 first.
     
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