1. ## Solving an Integral

i have big trouble solving this:

$\int sin(2x) cos(2x)$

i tried... trig. relations - failed for me
subsitution - failed for me
splitting the integral in two... - failed for me

derive gives me something completely different from my solution(s)

2. Originally Posted by coobe
i have big trouble solving this:
$\int sin(2x) cos(2x)$
What is the derivative of $\frac{{\sin ^2 (2x)}}
{4}?$

3. Originally Posted by coobe
i have big trouble solving this:

$\int sin(2x) cos(2x)$

i tried... trig. relations - failed for me
subsitution - failed for me
splitting the integral in two... - failed for me

derive gives me something completely different from my solution(s)
Note that $sin(2A) = 2sin(A)cos(A) \rightarrow sin(A)cos(A) = \frac{1}{2}sin(2A)$

It follows that in this case A=2x and so your problem reduces to

$\frac{1}{2}\int sin(4x)$

which should be easier

4. thats neat, thank you both for the quick reply!

i just realize that i need some refreshment on Trigonometry, will work on that before i dig deeper into integrals

5. Originally Posted by coobe
i have big trouble solving this:

$\int sin(2x) cos(2x)$

derive gives me something completely different from my solution(s)
You can derive a few trig equations by also doing u-substitution.
Try u=sin(2x) and w=cos(2x). Both work. Use different c's though and let x=0 afterwards to solve for those c's.