(10)
∫ dx/[x(x^2+1)]
let
1/[x(x^2+1)] ≡ A/x + (Bx+C)/(x^2+1)
=>
1 ≡ A(x^2+1) + (Bx+C)x
x=0, =>A=1
coef. of x^2
A+B=0
B=-1
coef. of x
C=0
∫ dx/[x(x^2+1)]
= ∫ [1/x -x/(x^2+1) ] dx
=ln|x | -(1/2)ln|x^2+1| +C
=ln| x/√(x^2+1) | + C
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