How do you integrate ln(x) with respect to x?

Rewrite ln(x) as 1ln(x) then integrate by parts.  The formula for integration by parts is ∫ uv' = uv - ∫ vu', here use u = ln(x) and v' = 1.  By differentiating u we get u' = 1/x, and by integrating v' we get v = x.  Putting these numbers into this formula gives ∫ 1ln(x) = xln(x) - ∫ x/x dx = xln(x) - ∫ 1 dx.  The integral of 1 is x, so the final answer is x*ln(x) - x + c, for a constant c.