InterviewSolution
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InterviewSolution
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`int(x-1)/((x+1)(x^(2)+1))dx` का मान ज्ञात कीजिए । |
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Answer» माना `(x-1)/((x+1)(x^(2)+1))` `" "=(A)/(x+1)+(Bx+C)/(x^(2)+1)` `" "=(A(x^(2)+1)+(Bx+C)(x+1))/((x+1)(x^(2)+1))` `rArr" "A(x^(2)+1)+(Bx+C)(x+1)=x-1` समान घातों के गुणांकों की तुलना करने पर `A+B=0` `B+C=1` `A+C=-1` हल करने पर `A=-1,B=1, C=0` `therefore int(x-1)/((x+1)(x^(2)+1))dx=int(-1)/(x+1)dx+int(x)/(x^(2)+1)dx` `=int(-1)/(x+1)dx+(1)/(2) int (2x)/(x^(2)+1)dx` `=-log|x+1|+(1)/(2)log|x^(2)+1|+c` |
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