Postati aici intrebari legate de problemele din aceasta varianta.

2 c

int[(x^2-1)/(x^2+x+1)x]dx de la 1..2 =
metoda coeficientilor

(x^2-1)/(x^2+x+1)x= (Ax+B)/(x^2+x+1) + C/x
numitor comun si factori se obtine
x^2-1=(A+C)x^2+(B+C)x+C
rezulta sistemul
A+C=1
B+C=0
C=-1
rezolvi si obtii A=1, B=1, C=-1
revii la int si
=int[(x+1)/(x^2+x+1)]dx de la 1..2 - int[(1)/x]dx de la 1..2=
= 1/2*int[(2x+2)/(x^2+x+1)]dx de la 1..2 - ln(x) bara 1..2=
=1/2ln(x^2+x+1) bara 1..2 -1/rad(3)*arctg [((2x+1)/2)/rad(3)] bara 1..2 - ln(2)=
=1/2 ln(7/3) -[1/rad(3)]* arctg(5/rad(3))+[1/rad(3)]*arctg(3/rad(3)) -ln2=...