intigration of -logX power of e ?

Question

method of this question

Answer 1

e^-log(x)=e^log(1/x).

If log(x) means ln(x), then e^log(1/x)=e^ln(1/x)=1/x, the integral of which is ln(x)+C (where C is the constant of integration). This can also be written ln(ax) or ln|ax| where a is a constant (C=ln(a)).