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Ujwal Prakash
Asked: 2022-10-29T00:59:04+05:30 In:

`int (dx)/(x(x^(2)+1))` बराबर है:
A. `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^()+1)+C`
D. `(1)/(2)log|x|+log(x(2)+1)+C`

`int (dx)/(x(x^(2)+1))` बराबर है:
A. `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^()+1)+C`
D. `(1)/(2)log|x|+log(x(2)+1)+C`
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  1. Correct Answer – A
    माना `(1)/(x(x^(2)+1))=(A)/(x)+(Bx+C)/(x^(2)+1)`
    `1=A(x^(2)+1)+(Bx+C)x`
    x = 0 तो `1=A(0+1)+0″ “rArr” “A=1`
    `x^(2)` के गुणांक समान रखने पर,
    `0=A+B” “rArr” “B=A=-1`
    `x` के गुणांक समान रखने पर , 0 = C
    `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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