5.5 The Substitution Rule/19

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\int {\frac {\left(\ln(x)\right)^{2}}{x}}dx\ =\ \int u^{2}du\\[2ex]&=\ {\frac {u^{2+1}}{2+1}}du\ =\ {\frac {1}{3}}u^{3}+C\\[2ex]u=\ln(x)du={\frac {1}{x}}dxdu={\frac {dx}{x}}&=\ {\frac {1}{3}}(\ln(x))^{3}+C\end{aligned}}}