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U-Substitution involving cos

  1. Apr 2, 2010 #1
    For this integration by substitution problem, I am not sure whether I should:

    1. simplify the problem first, then select U, find the derivative of U, then integrate


    2. use the product rule first (on the upper part of the equation), then select U, then find the derivative of U, then integrate,


    3. if I could just cancel like terms first, and be left with cos to integrate

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

    Evaluate the indefinite integral

    2. Relevant equations

    integral of cos * (square root of t) / (square root of t) dt

    3. The attempt at a solution

    integral of cos * (square root of t) / (square root of t) dt

    integral of [cos t^(1/2)] / t^(1/2) dt

    let U = cos t ^ 1/2

    du = 1/2 (sin t 3/2) / (t 3/2)

    Now I am really lost! What should I do?
  2. jcsd
  3. Apr 2, 2010 #2
    Try t = x^2
  4. Apr 2, 2010 #3
    Thanks for your reply Count Iblis. How does x come in this?
  5. Apr 2, 2010 #4
    It's just a variable name. If you prefer to use 'u' instead, make it t = u^2.
  6. Apr 2, 2010 #5
    Still trying to figure out what you mean by t = u^2.

    Up to where was I right?
  7. Apr 3, 2010 #6
    t = u^2 means you're going to use the substitution u = sqrt(t) to evaluate your integral. I'm pretty sure you can continue from there
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