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intsqrt(x^(2)-4x+2)dx=?...

`intsqrt(x^(2)-4x+2)dx=?`

A

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

B

` (x-2)sqrt(x^(2)-4x+2)+(1)/(2)log|(x-2)+sqrt(x^(2)-4x+2)|+C`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int sqrt((x-2)^(2)-(sqrt(2))^(2))dx`
`=(1)/(2)(x-2)sqrt(x^(2)-4x+2)-(2)/(2)log |(x-2)+sqrt(x^(2)-4x+2)|+C`
`=(1)/(2) (x-2)sqrt(x^(2)-4x+2)-log |(x-2)+sqrt(x^(2)-4x+2)|+C`
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