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Integrating with logs

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data

    ∫x(2^x^3)dx

    2. Relevant equations



    3. The attempt at a solution
    I've tried using substitution using both x^3 and 2^x^3 as u.

    I did get pretty far by using log_2 on each side.

    ∫log_2(x2^x^3)dx=∫(log_2(x)+log_2(2^x^3))dx=∫(log_2(x)+x^3)dx

    At this point I'm not sure what to do, any help or hints would be appreciated.
     
  2. jcsd
  3. Jan 26, 2014 #2

    SteamKing

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  4. Jan 26, 2014 #3

    Dick

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    Two points. i) you can't take log inside an integral and get anything having anything to do with the original integral. ii) 2^x^3 doesn't mean anything. You mean either (2^x)^3 or 2^(x^3). They are very different. I suspect you mean (2^x)^3. That you can do with some work and integration by parts. 2^(x^3) leads to a nonelementary integral.
     
  5. Jan 26, 2014 #4
    It was 2^(x^3) all multiplied by x.
     
  6. Jan 26, 2014 #5

    Dick

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    If your integrand is ##x 2^{(x^3)}## as opposed to ##x (2^x)^3## then you need some species of a gamma function to get an integral. Have you talked about those?
     
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