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Find the Indefinite Integral

  1. Jan 14, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗


    2. Relevant equations



    3. The attempt at a solution
    ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗
    ∫▒((4x^2)/(2x^(3/2) )+(2√x)/(2x^(3/2) )+1/(2x^(3/2) ))dx
    2∫▒x^(1/2) dx+∫▒〖x^(-1) dx〗+1/2 ∫▒x^(-3/2) dx
    2×2/3 x^(3/2)+ln⁡x+1/2×(-2) x^(-1/2)+C
    4/3 x^(3/2)+ln⁡x-x^(-1/2)+C
    4/3 √(x^3 )+ln⁡x-1/√x+C
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 14, 2013 #2

    SammyS

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    It looks good. Take the derivative to check it.
     
  4. Jan 15, 2013 #3
    Thanks
     
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