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int (dx)/(sqrt(2-4x+x^(2)))=?...

`int (dx)/(sqrt(2-4x+x^(2)))=?`

A

`log|(x-2)+sqrt(x^(2)-4x+2)|+C`

B

`log|x+sqrt(x^(2)-4x+2)|+C`

C

`log|x-sqrt(x^(2)-4x+2)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(dx)/(sqrt((x^(2)-4x+4)-2))=int(dx)/(sqrt((x-2)^(2)-(sqrt(2))^(2)))`
`=log |(x-2)+sqrt(x^(2)-4x+2)|+C.`
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