Question

How to find the indefinite integral of `sin(2x)cos(2x)dx`?

Answer 1

Use the double angle formula for the sine to rewrite it as

`int 1/2 sin(4x) dx`

and integrate by the substitution: `u= 4x` so `du=4dx`

Or leave it as is and use either:

`u=sin(2x)`, so `du=2cos(2x)dx`

OR

`u=cos(2x)`, so `du= - 2sin(2x)dx`

Any of these three methods will give you the correct answer. (Although they all look different!)