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Homework Help: Integration: Rationalizing and then Partial Fractions

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex][tex]\frac{e^xcos(log_7(e^x+9))}{(e^x+9)ln(7)}[/tex]dx


    2. Relevant equations



    3. The attempt at a solution
    Let u= (ex+9)
    du= exdx
    New integral [tex]\int[/tex][tex]\frac{cos(log_7(u))}{(u)ln(7)}[/tex]du
    This is where I got l little lost. Should I let log7(u)=[tex]\frac{ln(u)}{ln(7)}[/tex]? Or is this just a waste of time. I was thinking after that I would use log rules to make it ln(u)-ln(7) and then split it into two separate integrals and follow that by partial fractions. I'm just curious if I'm on the right track.
     
  2. jcsd
  3. Jul 15, 2010 #2
    Just let [tex]t=\log_7 u[/tex]. Then only constant times integral of cosine is left.
     
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