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

Explanation

माना `I=int(dx)/(2x^(2)-4x+1)=(1)/(2)int(dx)/(x^(2)-2x+(1)/(2))" "` (नोट कीजिए )
`=(1)/(2)int(dx)/(x^(2)-2x+1-1+(1)/(2))=(1)/(2)int(dx)/((x-1)^(2)-((1)/(sqrt2))^(2))`
माना `(x-1)=t therefore dx=dt` तथा `(1)/(sqrt2)=a`
`therefore" "I=(1)/(2)int(dt)/(t^(2)-a^(2))`
`=(1)/(2)(1)/(2a)log((t-a)/(t+a))=(1)/(4.(1)/(sqrt2))log[((x-1)-(1)/(sqrt2))/((x-1)+(1)/(sqrt2))]`
`=(1)/(2sqrt2)log[(sqrt2x-(sqrt2+1))/(sqrt2x-(sqrt2-1))]`