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Question
Find `int sqrt((x + 2)/(x - 2))` dx
Sum
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Solution
`int sqrt((x + 2)/(x - 2))` dx
`sqrt((x + 2)/(x - 2)) = (x + 2)/(sqrt(x^2 - 4))`
So,
`int sqrt((x + 2)/(x - 2)) = int (x + 2)/(sqrt(x^2 - 4))`
= `int x/(sqrt(x^2 - 4))dx + 2 int 1/(sqrt(x^2 - 4))dx`
= `sqrt(x^2 - 4) + 2 log |x + sqrt(x^2 - 4)| + C`
∴ `int sqrt((x + 2)/(x - 2)) dx = sqrt(x^2 - 4) + 2 log |x + sqrt(x^2 - 4)| + C`
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