Odpowiedź:
[tex]\huge\boxed{\int\dfrac{\ln x-2}{x}dx=\dfrac{1}{2}\ln^2x-2\ln x+C}[/tex]
Szczegółowe wyjaśnienie:
[tex]\int\dfrac{\ln x-2}{x}dx=\int\dfrac{\ln x}{x}dx-\int\dfrac{2}{x}dx=(*)\\\\\int\dfrac{\ln x}{x}dx\Rightarrow\left[\begin{array}{ccc}\ln x=t\\\dfrac{1}{x}dx=dt\end{array}\right] \Rightarrow\int tdt=\dfrac{1}{2}t^2=\dfrac{1}{2}\ln^2x\\\\\int\dfrac{2}{x}dx=2\int\dfrac{1}{x}dx=2\ln x\\\\(*)=\dfrac{1}{2}\ln^2x-2\ln x[/tex]
