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Math Help - Integration by parts, HELP!

  1. #1
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    Integration by parts, HELP!

    I'm supposed to integrate this:

    (x^5)cos(x^3)

    I understand to make u = x^5 in order to try and eliminate it, but that forces me to make dv = cos(x^3), which I am at a complete loss as to its integral. I snooped around on the net, and from some of my readings, it seems as though it requires a math program to do so(atleast the definite integral). My Ti-89 is of no help, so I come here...


    Please help, any bit of insight would be greatly appreciated...
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  2. #2
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    Quote Originally Posted by phack View Post
    I'm supposed to integrate this:

    (x^5)cos(x^3)
    This is a hard integral.
    If you call t=x^3 then t'=3x^2 thus you need an x^2.

    You split is as,
    \frac{1}{3} \int x^3 (3x^2) \cos x^3 dx
    Use substitution rule,
    \frac{1}{3} \int t\cos t dt
    Now, you need to do integration by parts.
    Let u=t and v'=\cos t.
    Thus, u'=1 and v=\sin t.
    Integration by parts,
    t\sin t - \int \sin t dt=t\sin t+\cos t+C
    Substitute back (and multiply by 1/3 from beginning),
    \frac{1}{3}x^3 \sin x^3+\frac{1}{3}\cos x^3 +C
    -------

    If you want a website to check your integration work,
    You can use The Integrator--Integrals from Mathematica
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  3. #3
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    Thankyou, you are a life saver...
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