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Integral and complex exponential question: my physics teacher just gives me math hw

  1. Oct 22, 2006 #1
    I have two homework problems that have been driving me nuts:

    1.) evaluate the indefinite integral:

    integral(dx(e^ax)cos^2(2bx))

    where a and b are real positive constants. I just don't know where to start on it.

    2.) Find all values of i^(2/3)

    So far I have:

    i^(2/3)
    = e^(2/3*ln(i))
    = e^(2/3*i*(Pi/2 + 2*n*Pi))
    = e^(i*Pi/3)*e^(i*n*4Pi/3)

    I know from the back of my book my three solutions should end up being (1+i*sqrt(3))/2, (1-i*sqrt(3))/2, -1. But I can't seem to get there. I'd really appreciate any help. Sorry if my shorthand is confusing.
     
  2. jcsd
  3. Oct 22, 2006 #2
    For 1) use the exponential notation for cos x, then integrate. You can do it by integration by parts twice, then use 'the trick' but that would be pretty messy.
     
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