Question

What is the antiderivative of `(2x)(sinx)(cosx)`?

Answer 1

We have that

#int (2x)(sinx)(cosx)dx=int x*sin2xdx= -1/2 int x (cos2x)'dx=-1/2*[xcos2x-intcos2xdx]= -1/2xcos2x+1/4*sin2x+c#