1. Finding indefinite integrals (without the integration constant).
How come the answer is not (cosx)(sinx)(x)??
What does (without the integration constant) mean?
remember if the integral of f is F then F ' = f
So differentiate cos(x)sin(x)*x and you won't get sin(x)cos(x)
Now I think you are thinking "integral of fg = integral of f times integral of g"
but this isn't correct.
There is no product rule for integration
But even for derivatives (fg) ' is not simply f ' g' is it ?
There are 2 ways to solve your integral
1, using u substitution let u = sin(x) or u = cos(x) either will work here
2.use the identity sin(x)cos(x) =1/2sin(2x) and use u = 2x