let
1/[[x(1+x^2)] ≡ A/x +(Bx+C)/(1+x^2)
=>
1≡ A(1+x^2) +(Bx+C)x
x=0, => A= 1
coef. of x^2
A+B=0
1+B=0
B=-1
coef. of x
C=0
1/[[x(1+x^2)] ≡ 1/x -x/(1+x^2)
∫(1->+∞) dx/[x(1+x^2)]
=∫(1->+∞) [1/x -x/(1+x^2) ] dx
=[ln|x/√(1+x^2)| ]| (1->+∞)
=-ln(1/√2)
=(1/2)ln2
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