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∫cos(x)^2 * tan(x)^3dx

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫cos(x)^2*tan(x)^3dx


    2. Relevant equations



    3. The attempt at a solution

    Were learning Integration by parts and u substitution but this one I can't figure out. I tried making it ∫cos(x)*(sin(x)^3)/(cos(x)^3)dx and then ∫tan(x)*sin(x)^2 but I don't know if I'm going in the right direction because I don't know how to solve from here.
     
  2. jcsd
  3. Feb 6, 2012 #2

    SammyS

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    Re: ∫cos(x)^2*tan(x)^3dx

    That should be [itex]\displaystyle \int\frac{\cos^2(x)\sin^3(x)}{\cos^3(x)}\,dx[/itex]

    The integrand can be simplified to:
    [itex]\displaystyle \frac{\sin^3(x)}{\cos(x)}[/itex]​
    Then change sin3(x) to (sin(x))(1-cos2(x))

    The integrand becomes:
    [itex]\displaystyle \frac{\sin(x)}{\cos(x)}-\sin(x)\cos(x)[/itex]​
     
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