x^2+4x+5=(x+2)^2+1 [m]∫ ^{1}_{0}\frac{1}{x^2+4x+5}dx= ∫ ^{1}_{0}\frac{1}{(x+2)^2+1}d(x+2)=arctg(x+2)|^{1}_{0}=arctg3-arctg2[/m]