Calculus

What is the best substitution to make to evaluate the integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx?

u = sin(2x)
u = cos(2x)
u = 2x
u = 5 − 2sin(2x)

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  1. This is more a question to interpret the words:
    " integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx"
    which turns out to be:
    ∫cos(2x)dx/√(5-2sin(2x))

    Check each case out by substituting u and du in the expression, and see which one seems to simplify most, or works best.

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