InterviewSolution
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InterviewSolution
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फलन `int(dx)/(1-x-x^(2))` का x के सापेक्ष समाकलन कीजिए । |
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Answer» माना `I=int(dx)/(1-x-x^(2))` `=int(dx)/(1-(x+x^(2)+(1)/(4)+(1)/(4)))" "` (पूर्ण वर्ग बनाने पर ) `=int(dx)/(1+(1)/(4)-(x+(1)/(2))^(2))=int(dx)/(((sqrt5)/(2))-(x+(1)/(2))^(2))` माना `x+(1)/(2)=t therefore dx=dt" तथा " (sqrt5)/(2)=a` `therefore" "I=int(dt)/(a^(2)-t^(2))` `=(1)/(2a)log((a+t)/(a-t))=(1)/(2(sqrt5)/(2))log[((sqrt5)/(2)+x+(1)/(2))/((sqrt5)/(2)-x-(1)/(2))]` `" "` (x तथा a के मान रखने पर ) `=(1)/(sqrt5)log((sqrt5+2x+1)/(sqrt5-2x-1))` |
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