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Solving integrals with the table of integrals

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫e2xarctan(ex)dx

    2. Relevant equations

    From the table of integrals:
    #92 ∫utan-1udu = (u2+1)/2)tan-1-u/2 + c

    or

    #95 ∫untan-1udu = 1/(n+1)[un+1tan-1-∫ (un+1du)/(1+u2) , n≠-1

    3. The attempt at a solution

    The answer is 1/2(e2x+1)arctan(ex) - (1/2)ex + C

    I don't know if I'm supposed to make a substitution first and if so what I should substitute and/or if which from I should use from the table. I've tried to make the initial substitution of e2x and ex and they both got me seemingly nowhere. Help please.
     
  2. jcsd
  3. Mar 8, 2012 #2

    LCKurtz

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    Try ##u=e^x## and see if you can't get it in a form to use 95 with ##u^n## in front for some ##n##.
     
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