Question

calculati urmatoarea integrala nedefinita :2x-3 supra x^2-3x+2 dx,x>2

Answer 1

$\int \frac{2x - 3}{ {x}^{2} - 3x + 2 } dx$

$= \int \frac{2x - 3}{ {x}^{2} - x - 2x + 2} \: dx = \int \frac{2x - 3}{x(x - 1) - 2(x - 1)} \: dx$

$= \int \frac{2x - 3}{(x - 2)(x - 1)} dx= \int \frac{x + x -2 - 1}{(x - 2)(x - 1)} \: dx$

$= \int \frac{x - 2 + x - 1}{(x - 2)( x- 1)} \: dx$

$= \int \frac{x - 2}{(x - 2)( x- 1)} \: dx + \int \frac{x - 1}{(x - 2)(x - 1)} \: dx$

$= \int \frac{1}{x - 1} \: dx + \int \frac{1}{x - 2} \: dx$

$= ln |x - 1| + ln |x - 2| + C$

$= ln( |x - 1| |x - 2| ) + C$