Question Number 152160 by peter frank last updated on 26/Aug/21
![∫[(1/(log x))−(1/((log x)^2 ))]dx](https://www.tinkutara.com/question/Q152160.png)
$$\int\left[\frac{\mathrm{1}}{\mathrm{log}\:\mathrm{x}}−\frac{\mathrm{1}}{\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\mathrm{dx} \\ $$
Answered by Olaf_Thorendsen last updated on 26/Aug/21
$$\mathrm{F}\left({x}\right)\:=\:\int\left(\frac{\mathrm{1}}{\mathrm{log}{x}}−\frac{\mathrm{1}}{\mathrm{log}^{\mathrm{2}} {x}}\right){dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\frac{\mathrm{log}{x}−\mathrm{1}}{\mathrm{log}^{\mathrm{2}} {x}}{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\frac{{d}}{{dx}}\left(\frac{{x}}{\mathrm{log}{x}}\right){dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\frac{{x}}{\mathrm{log}{x}}+\mathrm{C} \\ $$
Commented by puissant last updated on 26/Aug/21
$${jolie}\:! \\ $$
Commented by peter frank last updated on 26/Aug/21
$$\mathrm{thank}\:\mathrm{you} \\ $$