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?

a. u=sin(2x)
b. u=cos(2x)
c. u=2x
d. u=5-2sin(2x)

Answer 1

Can you type it out (sorry I always request this).

Answer 2

No your fine. I always forget to do that. One second

Answer 3

\[\int\limits_{}^{}\frac{ \cos(2x) }{ \sqrt{5-2\sin(2x)}} dx \] like this ?

Answer 4

Yes exactly lol

Answer 5

I'm always bad with these types of substitutions, I'd say work with the denominator and take out d. u=5-2sin(2x)
Let me double check.

Answer 6

well.. the point of u-substitution to cancel out something and makes the messy stuff looks easier
if i pick top part for u
and then take the derivative
u=cos(2x)
du= -2sin (2x)
\[\int\limits_{}^{}\frac{ \cos(2x) }{ \sqrt{5-2\sin(2x)}} dx \]
that doesn't make any sense. I can't cancel out anything
so u should be whatever under the sqrt