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Learning Trigonometric Substitution

  1. Sep 21, 2011 #1
    1. The problem statement, all variables and given/known data

    My book has given me this example, with a step by step, but one of the steps have left me dumbfounded, they seem to have left a huge gap in steps..

    2. Relevant equations

    3. The attempt at a solution

    [itex]\int sin^{5}xdx[/itex]

    [itex]\int sin^{4}x sinx dx[/itex]

    [itex]\int (1-cos^{2}x)^{2} sinx dx[/itex]

    [itex]\int (1 - 2cos^{2} x + cos^{4} x) sinx dx[/itex]

    Cool story bro. Here's the next step, what happened?

    [itex]= - cos x + \frac{2}{3}cos^{3}x - \frac{1}{5}cos^{5} x + C[/itex]

    Did they bring a negative out of the integral and do some kind of U substitution?
    Last edited by a moderator: Sep 21, 2011
  2. jcsd
  3. Sep 21, 2011 #2


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    Science Advisor
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    They put u = cos(x), du = -sin(x)dx. Try it.
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