Question

∫sin(x)cos(x) dx

Using the identity sin(2x) = 2 sin(x) cos(x)?

Answer 1

yes. so you have

1/2 ∫sin2x dx
let u = 2x, du=2dx and you have
1/4 ∫sinu du
= -1/4 cosu
= -1/4 cos(2x) + C