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How do I do this trig. integral?

  1. Jun 17, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫cos(x)^5 / sqrt(sin(x))dx


    2. Relevant equations
    ∫cos(x)^5 / sqrt(sin(x))dx


    3. The attempt at a solution

    i tried to break up cos(x)^5

    ∫(cos(x)^2)(cos(x)^3)dx

    I tried an identity

    (1-sin(x)^2)(sin(x)^-.5)cosx^3

    I tried to distribute the sin(x)^.5 and use a u sub but that's where I get stuck.
     
  2. jcsd
  3. Jun 17, 2014 #2

    Zondrina

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    Homework Helper

    Write the integral as:

    ##\int \frac{cos^4(x)cos(x)}{\sqrt{sin(x)}} dx##
    ##= \int \frac{(1-sin^2(x))^2cos(x)}{\sqrt{sin(x)}} dx##

    ##u = sin(x).. du = ..##
     
  4. Jun 17, 2014 #3
    I see, and du = cos(x)

    that takes care of my cos(x) in the numerator but it doesn't take care of the identity.
     
  5. Jun 17, 2014 #4

    Zondrina

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    Homework Helper

    Of course it does. If ##u = sin(x)## then ##u^2 = sin^2(x)##.
     
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