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Homework Help: Integration problem

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the integral of [tex]\int\frac{5dx}{\sqrt{25x^2 -9}}, x > \frac{3}{5}[/tex]



    3. The attempt at a solution

    First, I made x = 3/5 secx, and dx = 3/5 secxtanxdx

    [tex]\int\frac{3secxtanxdx}{5\sqrt{(9/25)(sec^2x -1)}}[/tex]

    [tex]\int\frac{secxtanxdx}{tanx}[/tex]

    [tex]\int secxdx[/tex]

    [tex]ln|secx + tanx| + C[/tex]

    [tex]ln|\frac{5x}{3} + \frac{5\sqrt{x^2 - \frac{9}{25}}}{3}| + C[/tex]

    The final step is my answer. However, when I try to integrate using the wolfram integration calculator, I get [tex]ln|2(\sqrt{25x^2 - 9} + 5x) + C[/tex]

    Where did I go wrong?
     
  2. jcsd
  3. Mar 28, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    Well I can't find an error in what you did but what I can say is that their answer can be reduced to


    ln2+ln|5x+√(25x2-9)|+C=ln|5x+√(25x2-9)|+A


    and your answer can be written as

    ln(1/3)+ln|5x+√(25x2-9)| = ln|5x+√(25x2-9)|+B

    So I would say that they are the same in essence.
     
  4. Mar 28, 2010 #3

    Mark44

    Staff: Mentor

    It's not a good idea to have a substitution variable with the same name as the variable it is a substitution for.
     
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