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Integration problem

  1. Nov 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Compute the following antiderivative [tex] \int (sin^3(x))(cos^4(x)) dx [/tex]

    2. Relevant equations

    3. The attempt at a solution
    If this problem requires use of integration by parts i'm struggling to work out to split it up and make it manageable. Have searched countlessly for a similar example on the net but have had no luck. Thanks
  2. jcsd
  3. Nov 27, 2007 #2


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    There is a standard "method" when you have a trig function to an odd power.

    Since sin(x) it to the 3rd power, take one out to use with dx, convert sin2(x) to cos:
    [tex]\int sin^3(x)cos^4(x)dx= \int sin^2(x)cos^4(x) sin(x)dx= \int (1- cos^2(x))cos^4(x) sin(x)dx[/itex]
    Now what substitution will make that easy?
  4. Nov 27, 2007 #3
    All you should do is new variable u = cos(x). You'll get integral u^4-u^6.
  5. Nov 27, 2007 #4
    Actually, [tex]u^6 - u^4[/tex] due to the negative in the derivative of [tex]cos(x)[/tex]
    Last edited: Nov 27, 2007
  6. Nov 27, 2007 #5
    fikus what do you mean, i can do a substitution straight away?
  7. Nov 27, 2007 #6
    you can once you find that the derivative of your substitution appears in your original problem
  8. Nov 27, 2007 #7


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    I believe that is what everyone as been trying to tell you!
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