Question

Найдите первообразную х-1/х+2

Answer 1

$\int\limits { \frac{x-1}{x+2} } \, dx = \left \{ {{t=x+2} \atop {dx=dt}} \right. = \int\limits{ \frac{t-3}{t} } \, dt= \int\limits { \frac{t}{t}- \frac{3}{t} } \, dt= \\ \\ =\int\limits {1} \, dt-\int\limits { \frac{3}{t} } \, dt=t-3ln|t| \\ \\ x+2-3ln|x+2|+C$