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Math Help - help bad integration problem

  1. #1
    Junior Member
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    Unhappy help bad integration problem

    ∫(cos2x+1/sin4x )

    can any one help me with this step by step solution cause i have fill 2 papers of failed attempts
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  2. #2
    Super Member
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    Is it \int \left(\frac{\cos{2x}+1}{\sin{4x}}\right)^2~dx

    or

    \int \left(\cos{2x}+\frac{1}{\sin{4x}}\right)^2~dx
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  3. #3
    Junior Member
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    it is the second one

    ∫(cos2x+(1/sin4x) )
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  4. #4
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    Expand \left(\cos{2x}+\frac{1}{\sin{4x}}\right)^2 to get:

    \int \cos^2{2x}~dx + \int \frac{2\cos{2x}}{\sin{4x}}~dx + \int \csc^2{4x}~dx

    Use the identity \cos^2{(2x)} = \frac{1+\cos{(4x)}}{2} and the first integral becomes trivial.

    Use the identity \sin{(4x)} = 2\sin{(2x)}\cos{(2x)} and the second integral becomes trivial.

    The third is trivial as it is.
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