Question

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)

Answer 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.