x²+4x+8 = (x+2)² + 4
(x+a)² +b = x²+2ax+a²+b
2ax = 4x => 2a = 4 => a=2
a²+b = 8 => 4+b = 8 => b = 4
Integrala din [tex] \frac{1}{ x^{2} +4x+8} [/tex] dx = integrala din [tex] \frac{1}{( x+2)^{2} +4} [/tex] dx = [tex] \frac{1}{2} * arctg \frac{x+2}{2} [/tex] luata de la -2 la 0
=[tex] \frac{1}{2} arctg 1 - \frac{1}{2} arctg 0 [/tex]
