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Evaluate the integral after figuring out the proper method to use

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫ ((2t+3)^2)/t^2 dt


    2. Relevant equations



    3. The attempt at a solution
    I figured that I would use integration by parts. The problem I'm having is that we haven't actually learned integration by parts, only the u substitution method. I went ahead and read the book on the proof and several examples, but its still a bit new to me so I'm not sure how to approach he problem.

    u=1/t^2
    du=-dt/3t^3

    ∫dv∫=(2t+3)^2 dt
    v=(4t^3)/3 +6t^2 +9t

    4t/3 +6+9/t - ∫ ((4t^3)/3 +6t^2 +9t)/t^3 dt

    Is there a more straight forward way of solving this?
     
  2. jcsd
  3. Dec 4, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure there is. Just multiply the numerator out. Then split it up and integrate.
     
  4. Dec 4, 2012 #3
    Oh wow..... Thanks for the help. I feel a little silly right now.
     
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