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int(dx)/(sqrt(x^2-3x+2))...

`int(dx)/(sqrt(x^2-3x+2))`

A

`log |(x-(3)/(2))+sqrt(x^(2)-3x+2)|+C`

B

`log | +sqrt(x^(2)-3x+2)|+C`

C

`log |x +sqrt(x^(2)-3x+2)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(dx)/(sqrt((x^(2)-3x+(9)/(4))-(1)/(4)))=int(dx)/(sqrt((x-(3)/(2))^(2)-((1)/(2))^(2)))`
`=int (dt)/(sqrt(t^(2)-((1)/(2))^(2)))=log |t+sqrt(t^(2)-(1)/(4))|+C,"where" (x-(3)/(2))=t`
`=log |(x-(3)/(2))+sqrt(x^(2)-3x+2)|+C.`
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