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Integrate the functions1/(sqrt((x-1)(x-2...

Integrate the functions`1/(sqrt((x-1)(x-2)))`

Text Solution

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` int(1)/(sqrt((x-1)(x-2)))dx`
`= int(1)/(sqrt(x^(2)-3x+2))dx`
`= int (1)/(sqrt((x^(2) -3x+(9)/(4))+2-(9)/(4)))dx`
`= int (1)/(sqrt((x-(3)/(2))^(2) -((1)/(2))^(2)))dx`
`=log | x-(3)/(2) +sqrt((x-(3)/(2))^(2) -((1)/(2))^(2))|+c`
` =log|x-(3)/(2) +sqrt(x^(2)-3x+2)|+c`
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