∫ ( ln ( x ) ) 2 x d x = ∫ u 2 d u = u 2 + 1 2 + 1 d u = 1 3 u 3 + C u = ln ( x ) d u = 1 x d x d u = f r a c d x x = 1 3 ( ln ( x ) ) 3 + C {\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}}}
![{\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/acd09daaa188e26f53b2f6f5ef60fed50903f18c)