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Math Help - Integral problem

  1. #1
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    Integral problem

    I'm trying to figure out the integral of (x^3)(sin x). Any pointers?
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  2. #2
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    Krizalid's Avatar
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    This one requires integration by parts three times.

    For start, set u=x^3 & dv=\sin x\,dx.
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by taichu View Post
    I'm trying to figure out the integral of (x^3)(sin x). Any pointers?
    are you allowed to use Integration by parts? i.e,
    \int udv = uv - \int vdu

    if so, do it three times..
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  4. #4
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    Haha, I just figured that out now, and came to post my solution.

    What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by taichu View Post
    Haha, I just figured that out now, and came to post my solution.

    What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.
    that is incorrect, i believe

    check the answer here
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  6. #6
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by taichu View Post
    Haha, I just figured that out now, and came to post my solution.

    What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.
    it should be
    x^3 \cos x + 3x^2 \sin x - 6x \cos x + 6 \sin x + C
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