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Quick integral

  1. May 10, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int cos^{2}(bx)dx[/itex]

    2. Relevant equations

    3. The attempt at a solution

    This integral popped up in my quantum mechanics class yesterday and I solved it through double substitution to get,
    [itex]\frac{x}{2} + sin(bx) * \frac{1}{4b}[/itex].

    My question is, someone in my class said there was an easier way to solve this that only took 2-3 lines. Does anyone here have any ideas on what that may be?
  2. jcsd
  3. May 10, 2012 #2


    User Avatar
    Gold Member

    Use double angle formula to convert the integrand.
    [tex]\cos 2(bx) = 2\cos^2 (bx) -1[/tex]
    [tex]\int cos^{2}(bx)dx=\frac{1}{2} \int (cos 2(bx)+1)dx[/tex]
  4. May 10, 2012 #3
    Re: Quick integral (Solved)

    Wow that makes it easier...haha always forget my trig identities. Cheers for the quick response.
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