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Question about this integral

  1. Mar 15, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta[/tex]

    3. The attempt at a solution

    i took [tex]u = ae^\theta-b[/tex] so [tex]e^\theta = \frac{u + b}{a}[/tex] then i substituded back into the integral and iget this

    [tex]\int \frac{u + b + b}{u} \, du[/tex]

    [tex]\int du +\int \frac{2b}{u} \, du[/tex]

    [tex]= u \du + 2b \ln u +C[/tex]

    [tex]= u + 2b \ln u +C[/tex]

    [tex]= ae^\theta-b + 2b\ln (ae^\theta-b) [/tex]

    but the answer of the book is
    [tex]\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta = 2\ln (ae^\theta-b) - \theta + C [/tex]
    what did i do wrong?
    Last edited: Mar 15, 2007
  2. jcsd
  3. Mar 15, 2007 #2


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    You didn't subsitute properly. You have to change dtheta too.
  4. Mar 15, 2007 #3
    write d0 as what it should equal to du
    for example if u=x^2
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