Mathematics

This integral combines a logarithm with a power of $x$ in the denominator—a classic setup for integration by parts. The key insight is to choose $u = \ln x$ (which becomes simpler when differentiated) and $dv = x^{-2}\,dx$ (which is easy to integrate). After applying the formula, you'll get a product term plus a remaining integral that's much more straightforward to evaluate.

This integral combines a logarithm with a power of $x$ in the denominator—a classic setup for integration by parts. The key insight is to choose $u = \ln x$ (which becomes simpler when differentiated) and $dv = x^{-2}\,dx$ (which is easy to integrate). After applying the formula, you'll get a product term plus a remaining integral that's much more straightforward to evaluate.