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Difficult integration

  1. Feb 6, 2008 #1
    integrate sin^4(2x) without using the reduction formula.im stuck.
    im pretty sure you have to use integration by parts.
  2. jcsd
  3. Feb 6, 2008 #2
    Try using double-angle formulae a couple of times.
  4. Feb 6, 2008 #3


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    The double angle formula for cos will help I believe.
  5. Feb 7, 2008 #4
    don't know what the reduction formula is, maybe it is the trick i'm about to give you

    [tex] \int sin(2x)^4 dx = \frac{1}{2} \int sin(u)^4 du = \frac{1}{2} \int (sin(u)^2)^{3/2} sin(u) du = \frac{1}{2} \int (1-cos(u)^2)^{3/2} sin(u)du = \frac{1}{2} \int (1-t^2)^{3/2} dt = \int sqrt((1-t^2)^3) [/tex]

    maybe you can do this???, of cause you have to keep track of all the substitutions to get how sin and y are related but that should be possible.
    Last edited: Feb 7, 2008
  6. Feb 7, 2008 #5
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