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

Evaluate `int(dx)/(sqrt(2-4x+x^(2)))`.

Text Solution

Verified by Experts

We have `int(dx)/(sqrt(2-4x+x^(2)))=int(dx)/(sqrt(x^(2)-4x+4-2))=int(dx)/(sqrt((x-2)^(2)-(sqrt(2))^(2)))`
`=log|(x-2)+sqrt((x-2)^(2)-2)|+C`
`=log|x-2+sqrt(x^(2)-4x+2)|+C`.
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