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How to integrate cos^3(x)

  1. Apr 27, 2008 #1
    What is the best way?
     
  2. jcsd
  3. Apr 27, 2008 #2
    Idk, you didn't show any work.
     
  4. Apr 27, 2008 #3
    I guess I'll have to use an identity. Maybe sin^2(x) = 1-cos^2(x)?

    (1-cos^2(x))*sin(x)

    u = 1- cos^2(x)

    du/dx = -2cos(x)sin(x)


    so that


    (1-cos^2(x))*sin(x) dx = (-u sin(x)/2cos(x)) du

    Doesn't really help, or?
     
  5. Apr 27, 2008 #4
    [tex]\int\cos x\cos^2 xdx[/tex]

    Use a BASIC trig identity to change the 2nd degree cosine function.
     
  6. Apr 27, 2008 #5
    not cosine, sine
     
  7. Apr 27, 2008 #6
    What are you talking about?
     
  8. Apr 27, 2008 #7
    Don't know, I guess I'm too drunk to do maths right now.
     
  9. Apr 27, 2008 #8
    Try again later :)
     
  10. Apr 27, 2008 #9
    Oh, I wrote cos^3 x instead of sin^3 x in the headline. That explains my confusion.

    sin^3 x

    =

    sin^2 x*sin x

    =

    (1 - cos^2 x)sin x

    Then substitution?

    u = 1-cos^2 x

    du/dx = 2cos x*sin*x

    so that

    sin^3 x dx = - u / 2cos x

    Hm...
     
  11. Apr 27, 2008 #10
    distribute the sinx and you'll see your solution
     
  12. Apr 28, 2008 #11

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    So how about just u= cos(x)?

    You know what they say "Don't drink and derive"!
     
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