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Integral of a function gives me acrtan(2cot(x)). How to evaluate this?

  1. Apr 24, 2013 #1
    Function is context is:
    $$\int \frac{(sin^22x)}{(4(1+3cos^2(x)))}dx$$

    And according to wolframalpha (I wasn't able to integrate this by myself) this integral is equal to

    $$\frac{5 x}{18} + \frac{(2 arctan(2 cot(x)))}{9} - \frac{sin(2 x)}{12}$$

    The above integral is the integral of a power function with respect to time.
    And I wanted to evaluate this between [0,60]; but the problem is when evaluating the cot(x) at 0 this give me infinity which make the fraction in the middle ∏/9. But according to the physics of the equation there should not be any energy generated at time = 0 as nothing is happening at time 0. so what is going on??

    Last edited: Apr 24, 2013
  2. jcsd
  3. Apr 24, 2013 #2


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    Plus a constant... and what you've done is figure out what that constant is
  4. Apr 24, 2013 #3


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    What does [0,60] represent? Does it have units?
  5. Apr 24, 2013 #4
    Not trying to be rude but in my original post I said "integrating with respect to time" so I didn't type time again; I thought it would be unnecessary.
  6. Apr 24, 2013 #5
    That makes sense. I completely forgot about the constant. Thanks!
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