`int (dx)/(2x^(2)-4x+1)` का मान ज्ञात कीजिए।

Answer

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Explanation

`int 1/(2x^(2)-4x+1) dx =1/2 int (1)/(x^(2)-2x+1/2) dx=1/2 int (1)/((x-1)^(2)-1/2) dx`
`=1/2 int (1)/((x-1)^(2)-(1/sqrt(2))^(2)) dx," "{:("मान लीजिए",x-1=t),(,dx=dt):}`
`=1/2 int 1/(t^(2) -(1/sqrt(2))^(2)) dx`,
`=1/2 1/(2 1/sqrt(2)) log |(t-1/sqrt(2))/(t+1/sqrt(2))|+c`
`=1/(2sqrt(2)) log |(sqrt(2)(x-1)-1)/(sqrt(2)(x-1)+1)|+c`
`=1/(2sqrt(2)) log |(sqrt(2)x-(sqrt(2)+1))/(sqrt(2) x-(sqrt(2)-1))|+c`