InterviewSolution
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InterviewSolution
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`int (dx)/(x(x^(2)+1))" equals "`A. `log|x|+(1)/(2)log(x^(2)+1)+C`B. `-log|x|+(1)/(2)log(x^(2)+1)+C`C. `(1)/(2)log|x|+log (x^(2)+1)+c`D. |
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Answer» Correct Answer - A `" 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 Equating the coefficient of `x^(2)` `0= A+B rArr B=- A=-1` Equating the coefficeints of `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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