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Math Help - Inntegrate

  1. #1
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    Inntegrate

    (cosx)^n
    integrate please!!!!
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  2. #2
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    Why?


    Any Calculus text book has a recursive formula for this. Look it up.
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  3. #3
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    You should specify your "n".
    Is it a positive integer?
    \int cos^{n}(x) dx = \int cos^{n-1}(x) cos(x) dx
    Use integration by parts.
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  4. #4
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    Quote Originally Posted by bhuang View Post
    (cosx)^n
    integrate please!!!!
    \int{\cos^n{x}\,dx} = \int{\cos^2{x}\cos^{n - 2}{x}\,dx}

     = \int{(1 - \sin^2{x})\cos^{n - 2}{x}\,dx}

     = \int{\cos^{n - 2}{x}\,dx} - \int{\sin^2{x}\cos^{n - 2}{x}\,dx}.


    Now use integration by parts on the second integral, with u = \sin{x} and dv = \sin{x}\cos^{n - 2}{x}.
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