InterviewSolution
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InterviewSolution
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फलन `int(dx)/(2x^(2)+x-1)` का x के सापेक्ष समाकलन कीजिए । |
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Answer» माना `I=int(dx)/(2x^(2)+x-1)=(1)/(2)int(dx)/(x^(2)+(1)/(2)x-(1)/(2))` `=(1)/(2)int(dx)/(x^(2)+(1)/(2)x+(1)/(16)-(1)/(16)-(1)/(2))" "` (पूर्ण वर्ग बनाने पर ) `=(1)/(2)int(dx)/((x+(1)/(4))^(2)-((3)/(4))^(2))` माना `x+(1)/(4)=t therefore dx=dt` तथा `(3)/(4)=a` `therefore" "I=(1)/(2)int(dt)/(t^(2)-a^(2))=(1)/(2.2a)log((t-a)/(t+a))` `=(1)/(4xx(3)/(4))log[(x+(1)/(4)-(3)/(4))/(x+(1)/(4)+(3)/(4))]=(1)/(3)log[(2x-1)/(2(x+1))]` |
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