f(x) = (1/2)sin2x
So, the antiderivative of f(x) = -(1/4)cos2x + c
You have asked this question four times already. I have answered it in four different ways. On top of all the other answers youve received. And you keep deleting your question. I think it just proves how small you are. Either youre too dumb to understand the answers youre getting, or you are jealous and resentful of the people who can or do answer. Im sorry for you that you are too arrogant to leave a question online for the world to see.
Anti derivative of sinx cox can be calculated as follows:
Use logarithmic equation: sin(2x) = 2 sinx cosx, therefore, sin(2x) / 2 = sinx cos x
∫sinx cosx dx = ∫ sin(2x)/2 dx = (1/2) ∫ sin(2x) dx = (1/2) (-1/2) cos(2x) + C
Solution: (-1/4)cos(2x) + C
Let u = sin x, then du = cos x dx.
Substitute you have integral u du = u^2/2 + C.
Subing back gets you: (sin^2 x)/2 + C