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

We can use substitution for this one. Take y=ln(x) to be equal to y= 1 x ln(x)Set u=ln(x) and dv/dx=1Compute du/dx and v:du/dx=1/x and v=xUse given formula - ∫ udv/dx dx = uv - ∫ vdu/dx dx= xln(x) - ∫ x/x dx= xln(x) - x (+C)This is the complete proof, however this is an easy one to remember and may be useful to memorise.