Integrate, with respect to x, xCos3x

Integration by parts:
u = x u' = 1v' = Cos3x v = (Sin3x)/3 + c
So, ∫xCos3x= (XSin3x)/3 - ∫(Sin3x)/3 dx= (XSin3x)/3 - 1/3( - (Cos3x)/3) + c = (XSin3x)/3 + (Cos3x)/9 + c