InterviewSolution
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InterviewSolution
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`int(dx)/(x(x^(2)+1))` is equal toA. `log|x|-(1)/(2)log(x^(2)+1)+C`B. `log|x|+(1)/(2)log(x^(2)+1)+C`C. `-log|x|+(1)/(2)log(x^(2)+1)+C`D. `(1)/(2)log|x|+log(x^(2)+1)+C` |
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Answer» Correct Answer - A Let `(1)/(x(x^(2)+1))=(A)/(x)+(Bx+C)/(x^(2)+1)` `rArr" "1=A(x^(2)+1)+(Bx+C)x=(A+B)x^(2)+Cx+A` On equating the coefficients of `x^(2),x` and constant term on both sides, we get `A+B=0, C=0` and `A=1` On solving these equations, we get `A=1, B=-1 and C=0` `therefore" "(1)/(x(x^(2)+1))=(1)/(x)+(-x)/(x^(2)+1)` `therefore" "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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