Question

cum se calculeaza integrala din lnx/x

Answer 1

$I= \int {\ \frac{\ln x}{x} } \, dx =\int {\ (\ln x)'\ln x } \, dx=\ln x\cdot\ln x-\int {\ \frac{\ln x}{x} } \, dx=\ln^2x-I \\ I=\ln^2x-I \\ 2I=\ln^2x \\ I= \frac{\ln^2x}{2}$