Ok I have to integrate -->∫cos(lnx) dx. could I use cos =U, -sinx=du, dv=lnxdx, v = 1/x I know the difference technically, but in this situation it is kinda weird. because the formula f(x)g(x)= uv-∫vdu. I thinking if they were number like 9(3) it would equal 27 so f(g) = f times G? but then that would mean ∫cos(lnx)dx = ∫cosxlnxdx . Which I don't think is right. last guess: could you do cos(lnx)= U, -sinx(lnx) times (1/2) dx = du, DV = lnxdx, v =1/x So I'm confused. I asked by teacher, because my first taught was to do U-substituion then integrate by parts. She said that would work, but it would end up being alot of ugly calculations. and that you could just integrate by parts directly. So if you could explain that, that would nice.