Integrate ln(x).

When tackling an unobvious integral question, first run through all the possible methods. I will now list the methods of integration: Substitution: could use this method, but it wouldn’t be particularly helpful as we wouldn’t be “getting rid of” any undesirable elements Reverse chain rule: no obvious integrals spring to mind! By parts: this seems like a fitting method Partial fraction expansion: not applicable Using trigonometric identities: not applicable Clearly, the best method to use would be integration by parts. Let u=ln(x), dv/dx=1/x, then du/dx=1, v=x. Then using the formula the integral of ln(x) = xln(x) - integral of x(1/x) = xln(x) -x + C (don’t forget the +C for indefinite integration!)