Problema 4

Să se calculeze $l=\lim_{\alpha\to\infty}\displaystyle\int_0^{\alpha}\dfrac{2x+1}{x^4+2x^3+3x^2+2x+2}\,dx$.

a) $l=\dfrac{\pi}{3}$; b) $l=\operatorname{arctg} 2$; c) $l=\dfrac{\pi}{2}$; d) $l=\operatorname{arctg}\dfrac{1}{3}$; e) $l=\operatorname{arctg} 3$; f) $l=\dfrac{\pi}{4}$.