∫ от ∞ до 0, ∫ x^2*dx/(x^2+1)*(x^2+4)
x^2= (Ax+B)*(x^2+4)+(Mx+N)*(x^2+1)
A+M=0
B+N=1
4A+M=0
4B+N=0
A=-M=0
N=4/3
B=-1/3
∫ ^(+ ∞)_(0) x^2·dx/(x^2+1)·(x^2+4)=
=-(1/3)∫ ^(+ ∞)_(0)dx/(x^2+1)+(4/3)∫ ^(+ ∞)_(0)dx/(x^2+4)=
=(-1/3)*(arctgx)|(+ ∞)_(0) + (4/3)*(1/2)arctg(x/2)|(+ ∞)_(0)=
=(-1/3)*(π/2)+(4/3)*(π/2)=π/2