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Integrate the following functions 1/ sqr...

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

Text Solution

Verified by Experts

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