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Question
Integrate the function `1/sqrt((x -1)(x - 2))`
Solution
Let `I = 1/sqrt((x - 1) (x - 2)) dx`
`= int dx/sqrt(x^2 - 3x + 2)`
`= int dx/sqrt((x^2 - 2 * 3/2 x + 9/4) + 2 - 9/4)`
`= int dx/sqrt((x - 3/2)^2 - 1/4)`
`= int dx/sqrt((x - 3/2)^2 - (1/2)^2)`
`= log abs ((x - 3/2) + sqrt ((x - 3/2)^2 - (1/2)^2)) + C` `...[∵ int dx/ sqrt(x^2 - a^2) = log |x + sqrt (x^2 - a^2)| + C]`
`= log |(x - 3/2) + sqrt((x - 1) (x - 2))| + C`
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