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Math Help - indefinite trigonometric integral

  1. #1
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    indefinite trigonometric integral

    \int \frac {\cos^5 x}{sqrt(sin x)} dx

    I haven't been able to figure out a way to deal with the square root in the denominator.

    The solution the book provides makes it clear that i should be using a Pythagorean identity in the usual way.
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  2. #2
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    Re: indefinite trigonometric integral

    Look at \int \frac{(\cos^2(x))^2(\cos(x))}{\sqrt{\sin(x)}}dx.

    I get there by saying to myself: "I'd *like* to substitute u = \sin(x) to simply that ugly denominator. That means I need du = \cos(x)dx. OK, I'll peel one of those cosines in the numerator off and put it with the dx. If I'm lucky, the rest of the numerator can be expressed in terms of u. Looking at it, I see that I am indeed lucky."
    Last edited by johnsomeone; October 1st 2012 at 11:29 AM.
    Thanks from MarkFL
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