Question

найти интеграл

int (x-11)/(2*x^2+5*x+3)dx 

Answer 1

int (x-11)/(2*x^2+5*x+3)dx=int(x-11)/(2x+3)(x+1)dx=

A/(2x+3)+B/(x+1)=Ax+A+2Bx+3B/(x+1)(2x+3)

A+2B=1

A+3B=-11

B=-12

A=25

 

=25int1/(2x+3)dx-12int1/(x+1)dx=25/2ln|2x+3|-12ln|x+1|