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Math Help - Integrating Trigonometric Functions With Powers

  1. #1
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    Integrating Trigonometric Functions With Powers

    Please explain the method of integrating trigonometric functions which have a power to them like cos54 (x). I have heard that only even powered trig functions have a method for solving them. For odd powered trig functions you have to break them down into a product like to integrate cos3 (x). You will write cos(x) times cos2(x) And use the formula of integration by parts. Is that correct?
    And what about trig functions with a power positive but less than one like cos0.8(x).
    What about trig functions like cos2.8(x) .
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  2. #2
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    Re: Integrating Trigonometric Functions With Powers

    This is essentially the same question you asked in "http://mathhelpforum.com/calculus/221129-equations-trigonometric-functions.html". Please do not post the same question twice.
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    Re: Integrating Trigonometric Functions With Powers

    Quote Originally Posted by HallsofIvy View Post
    This is essentially the same question you asked in "http://mathhelpforum.com/calculus/221129-equations-trigonometric-functions.html". Please do not post the same question twice.
    Sorry about that. Just trying to make it easier by dividing the question into positive and negative parts. Otherwise people might get fed up with the ongoing endless rant question.
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    Re: Integrating Trigonometric Functions With Powers

    Quote Originally Posted by reindeer7 View Post
    Please explain the method of integrating trigonometric functions which have a power to them like cos54 (x).
    in theory, if its only an indefinite integration, you can always use the reduction formulas to reduce the powers and then integrate.
    Integration by reduction formulae - Wikipedia, the free encyclopedia
    the result would be terribly long in this case.

    Quote Originally Posted by reindeer7 View Post
    What about trig functions like cos^{2.8} (x)
    I don't think that these can be integrated by using elementary functions...at least wolfram alpha thinks so...
    Integrate cos^2.8 x - Wolfram|Alpha
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