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Integration involving trig functions and various powers of X

  1. Sep 3, 2012 #1
    ∫[6x^6 sin (9x)]/[1+x^10] * dx

    I've set u =x^6
    du=6x^5*dx
    dx=du/6x^5

    ∫[6x^6 sin (9x)]/[1+x^10] * (du/6x^5)
    =
    ∫[x*sin(9x)*du]/1+x^10.

    Can someone help me figure out the next step? I'm thinking of putting a constant out in front, so I can use 2du for (x^10)
     
    Last edited: Sep 3, 2012
  2. jcsd
  3. Sep 3, 2012 #2

    SammyS

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    I doubt that this will work. That's a messy integral.

    However, you haven't finished the substitution ! You should end up with an integral in the variable, u, with no x what-so-ever.

    Are you sure you have written the problem correctly?

    What topics are you currently covering in whatever class this problem is from?
     
  4. Sep 3, 2012 #3
    Yeah, sadly I have written it down properly. Right now we're covering how to solve definite integrals with the use of substitution; it's a beautiful thing when it works, but these problems are moral-breakers. It's acually:

    ∫ 6x^6 sin(9x)/[1+x^10] *dx

    with the upper limit set at pi/2, and the lower limit at -pi/2.

    I excluded the limits part because I felt once I got help with the substitution, I had the problem down. But finding the right u is very difficult.
     
  5. Sep 3, 2012 #4

    SammyS

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    Having it be a definite integral makes all the difference in the world!

    Is the integrand either an even or an odd function?
     
  6. Sep 3, 2012 #5
    A glimpse of hope! I believe the integrand is an even function. Because when I plugged in f(-x), everything came out to be the same
     
  7. Sep 3, 2012 #6

    SammyS

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    Not quite!

    sin(-9x) = -sin(9x)

    Graph the integrand.
     
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