int (dx)/(x(x^(2)+1))" equals"

1.	int (dx)/(x(x^(2)+1))" equals"
Answer» `log\|x\|+(1)/(2)log(x^(2)+1)+C` `-log\|x\|+(1)/(2)log(x^(2)+1)+C` `(1)/(2)log\|x\|+log (x^(2)+1)+c` Solution :`" Let " (1)/(x(x^(2) +1))+(A)/(x)+(Bx+c)/(x^(2)+1)` 1=A `(x^(2) +1) +(Bx+c)x` x=0 then 1=A (0+1) +0 `RARR ` A=1 Equatingthe COEFFICIENT of `x^(2)` `0= A+BrArrB=- A=-1` Equatingthe coefficeintsof `x,0 =C` ` :. (1)/(x(x^(2) +1)) =(1)/(x)+ (-x)/(x^(2) +1)` ` :. int(1)/(x(x^(2)+1))DX = int ((1)/(x)-(x)/(x^(2)-1))dx` `=log \|x\|-(1)/(2) log (x^(2)+1)+c`

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