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Math Help - Integration Substitution

  1. #1
    Junior Member
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    Integration Substitution

    Hi. Stuck on this substitution. The integral is

    (x (cos(x/3))^(-1))/(9-x^2)^(1/2)

    The substitution is x=3cos(u)

    After performing the substitution the answer gives

    the integral.

    (3cos(u) u - 3sin (u) du)/3 sin (u)

    I arrived here OK, however it states that the above tidies to

    -3 u cos(u) du

    Stuck here on how it tidies to this
    Thanks
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by minicooper58 View Post
    Hi. Stuck on this substitution. The integral is

    (x (cos(x/3))^(-1))/(9-x^2)^(1/2)

    The substitution is x=3cos(u)

    After performing the substitution the answer gives

    the integral.

    (3cos(u) u - 3sin (u) du)/3 sin (u)

    Thanks
    after sub x=3cosu

    \int \frac{3u\cos u (-3\sin u)}{3\sin u}\cdot du not \int \frac{3u\cos u -3\sin u}{3\sin u}\cdot du

    the operation is Multiplication not subtraction
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