Question

Integrala nedefinita din 1/(x-1) = ??; x>1

Answer 1

[tex] \int\limits \frac{1}{x-1} \, dx x-1= t (x-1)'dx= t'dt dx=dt \int\limits \frac{dt}{t} \, dx= \int\limits \frac{1}{t} \, dt= ln |t| +C = ln | x-1| +C [/tex]