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Integration of a composite function

  1. Jun 18, 2012 #1
    1. The problem statement, all variables and given/known data
    The question I have is a more general one, but one I can't find an anser to since I don't have any access to a book on integration at the moment.

    How do we Integrate a composite function.

    ∫f(g(x)) dx

    2. Relevant equations

    3. The attempt at a solution
     
  2. jcsd
  3. Jun 18, 2012 #2

    micromass

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    A technique that might work is substitution. But it depends on the specific values of f and g, really.
     
  4. Jun 19, 2012 #3
    Ok, so that means that there is not general method like for integration, as there is for differentiation?
    Nonetheless thanks!
     
  5. Jun 19, 2012 #4
    If you have ∫f(g(x))g'(x)dx, then this is equal to the simpler ∫f(u)du. This is the analogue to the chain rule for integrals. I say it in words as, the derivative of the inside must appear outside.
     
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