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1/[x(x^2+1)] ≡ A/x +(Bx+C)/(x^2+1)
1≡ A(x^2+1) +x(Bx+C)
x=0, =>A =1
coef. of x^2
A+B=0
B=-1
coef. of x , =>C=0
∫(1->∞) dx/[x(x^2+1)]
=∫(1->∞) [1/x - x/(x^2+1)] dx
= [ln|x /√(x^2+1)|]| (1->∞)
= ln1 - ln(1/√2)
=(1/2)ln2
1/[x(x^2+1)] ≡ A/x +(Bx+C)/(x^2+1)
1≡ A(x^2+1) +x(Bx+C)
x=0, =>A =1
coef. of x^2
A+B=0
B=-1
coef. of x , =>C=0
∫(1->∞) dx/[x(x^2+1)]
=∫(1->∞) [1/x - x/(x^2+1)] dx
= [ln|x /√(x^2+1)|]| (1->∞)
= ln1 - ln(1/√2)
=(1/2)ln2
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