How do I integrate by parts?

When we integrate by parts, we begin by setting the first term to equal some variable U, the second term in the integral we set to be dv/dx. Then we differentiate the U to obtain du/dx and integrate dv/dx to obtain V. The next stage is to put in the values into the following formula: I = uv - ∫(v.du/dx) dx. Finally we integrate V . du/dx and then simplify the expression to obtain the solution to the integral. For an indefinite integral we add the constant (+C) and for a definite integral we have to sub in the limits accordingly. For example: ∫ (xlnx) dx        (1)  u=lnx     (2)  dv/dx=x    (3)  du/dx=1/x   (4)  v= ∫(dv/dx) dx = ∫ x dx = 0.5x^2 using the formula I = uv - ∫ (du/dx . v) dx we obtain ∫ (xlnx) dx = 0.5x^2 (lnx) - ∫ (1/x . 0.5x^2) dx = 0.5x^2 (lnx) - 0.5 ∫ x dx = 0.5x^2lnx - 0.25x^2 +C