Question

Найдите первообразную
х-1/х+2

Answer 1

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