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Evaluate: int1/(sqrt((x-2)(x-3)))dx...

Evaluate: `int1/(sqrt((x-2)(x-3)))dx`

Text Solution

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