InterviewSolution
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InterviewSolution
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`int(2x)/((x^(2)+1)(x^(2)+2))dx` का मान ज्ञात कीजिए । |
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Answer» माना `I=int(2x)/((x^(2)+1)(x^(2)+2))dx` `=int(1)/((t+1)(t+2))dt" माना "x^(2)=t` `" "rArr 2x dx = dt` माना `(1)/((t+1)(t+2))=(A)/(t+1)+(B)/(t+2)` `=(A(t+2)+B(t+1))/((t+1)(t+2))` `rArr" "A(t+2)+B(t+1)=1` `t=-1` रखने पर `A(-1+2)+0=1` `rArr" "A=1` `t=-2` रखने पर `0+B(-2+1)=1` `rArr" "B=-1` `therefore" "I=int(1)/(t+1)dt-int(1)/(t+2)dt` `=log|t+1|-log|t+2|+c` `=log|(t+1)/(t+2)|+c=log|(x^(2)+1)/(x^(2)+2)|+c` |
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