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Integrate e^2x / SQRT (e^2x + 3)

  1. May 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate e^2x / SQRT [(e^2x) + 3)]

    2. Relevant equations



    3. The attempt at a solution

    i know the solution, is: SQRT [(e^2x) + 3]

    but i have no idea why. Please I need help

    thank you
     
  2. jcsd
  3. May 20, 2010 #2
    Have you tried substitution?
     
  4. May 20, 2010 #3
    yes, t=e^2x + 3 but still nothing
     
  5. May 20, 2010 #4
    Ok, if t=e^2x + 3 then dt = 2e^2x, and what does the integral become in terms of t and dt?
     
  6. May 20, 2010 #5
    i have 1/2 (dt/ sqrt t)

    so 1/2 t^(3/2) / (3/2)

    then sqrt t / 3

    then sqrt (e^2x+3)^3 / 3

    its not the solution, it may be sqrt (e^2x+3)
     
  7. May 20, 2010 #6
    Close, you have 1/2(dt/sqrt(t)) = 1/2 t^(-1/2) dt. You integrated 1/2 t^(1/2) dt instead
     
  8. May 20, 2010 #7

    Gib Z

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    Homework Helper

    sqrt t is in the Denominator! So the power of t isnt 1/2, but actually... ?
     
  9. May 20, 2010 #8
    its true!!!!!! lol, it was my mistake, i forgot the change t^1/2 -> t^-1/2

    thank you!!
     
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