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Integrate the functions1/(sqrt((x-a)(x-b...

Integrate the functions`1/(sqrt((x-a)(x-b)))`

Text Solution

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`int(1)/(sqrt((x-a)(x-b)))dx`
`=int(1)/(sqrt(x^(2)-x(a+b)+ab))dx`
`=int(1)/(sqrt((x-(a+b)/(2))^(2)-((a-b)/(2))^(2)))dx`
` =log |x-(a+b)/(2)+`
`sqrt((x-(a+b)/(2))^(2)-((a-b)/(2))^(2))|+c`
`log |x-(a+b)/(2) +sqrt((x-a)(x-b))|+c`
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