differentiation

I am pretty confused with my solution to this integration proof question. I feel like it isn't the right way to prove it. d/dx (uv) = u(dv/dx)+v(du/dx) take the integral with respect to x of both sides: uv = ∫ u(dv/dx ) dx + ∫ v(du/dx) dx therefore, ∫ u(dv/dx ) dx = uv - ∫ v(du/dx)...