1.

फलन `int(dx)/(sqrt(1-4x-2x^(2)))` का x के सापेक्ष समाकलन कीजिए ।

Answer» माना `I=int(dx)/(sqrt(1-4x-2x^(2)))`
`=int(dx)/(sqrt(1-2(x^(2)+2x+1-1))" "` (नोट कीजिए )
`=int(dx)/(sqrt(3-2(x+1)^(2)))=(1)/(sqrt2)int(dx)/(sqrt((sqrt((3)/(2)))^(2)-(x+1)^(2)))`
माना `" "x+1=t rArr dx=dt`
तथा `" "sqrt((3)/(2))=a`
`therefore" "I=(1)/(sqrt2)int(dt)/(sqrt(a^(2)-t^(2)))=(1)/(sqrt2)sin^(-1)((t)/(a))`
`=(1)/(sqrt2)sin^(-1)[(sqrt2(x+1))/(sqrt3)]`


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