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Integration of trigonometric function

  1. Jan 9, 2016 #1
    1. The problem statement, all variables and given/known data
    I have included the LaTex version of the problem.
    [itex]\int \frac{sin^2 x}{1+cos^2 x} dx[/itex]

    2. Relevant equations
    Simplifying fraction
    Partial fractions

    3. The attempt at a solution
    I have uploaded my attempt at the solution. WIN_20160109_14_54_21_Pro.jpg WIN_20160109_14_53_38_Pro.jpg
     
  2. jcsd
  3. Jan 9, 2016 #2

    LCKurtz

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    I don't usually read handwritten solutions, and I never read ones printed sideways. Regarding your integral, I would suggest suggest using the double angle cosine formulas for your squared trig functions. This will give you a rational function of ##\cos(2x)##. Then the tangent half angle substitution will help you out. See:

    https://en.wikipedia.org/wiki/Tangent_half-angle_substitution
     
  4. Jan 9, 2016 #3

    SteamKing

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    Partial fractions and trig functions usually don't go together. Partial fractions are typically used to simplify rational expressions of a single variable.

    For integrating rational expressions of trig functions, a typical approach is to simplify using a trig identity of some sort first, and then try to use either u-substitution or integration by parts, if those techniques might be useful.
     
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