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Question
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Solution
Let I = `int 1/sqrt((x - 3)(x + 2)).dx`
= `int 1/sqrt(x^2 - x - 6).dx`
= `int 1/sqrt((x^2 - x + 1/4) - 1/4 - 6).dx`
= `int 1/sqrt((x - 1/2)^2 - (5/2)^2).dx`
= `log|(x - 1/2) + sqrt((x - 1/2)^2 - (5/2)^2)| + c`
= `log|(x - 1/2) + sqrt(x^2 - x - 6)| + c`.
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