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Homework Help: Integration by parts

  1. Jan 31, 2006 #1
    Integration by parts :(

    hi I have been trying this question for quite a while now and am unsure of what to do. Any help would be apprectiated.

    Integral x^13 cos(x^7) dx

    I know you have to use integration of parts. Here is what i have done so far:

    let U=x^3
    dU =13x^12 dx

    dV=cos(x^7)
    V=?
    First off I cant manage to find the antiderivative of cos(x^7)

    After finding that i think you use
    integral u(dV) = uv - v(dU)
     
  2. jcsd
  3. Jan 31, 2006 #2
    Rewrite the integral as (x^7 * x^6) * cos (x^7). Then let u = x^7. Then du = 7x^6 dx. So the integral becomes:

    (1/7) ยง u cos(u) du

    Which you can integrate by parts. Then substitute u back in and you're done.
     
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