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Question
Integrate the following with respect to x.
`1/(x^2 - x - 2)`
Solution
`int 1/(x^2 - x - 2) "d"x`
Cosier `x^2 - x - 2 = x^2 - 2x(1/2) + 1/4 - 1/4 - 2`
= `(x - 1/2)^2 - 9/4`
= `(x - 1/2)^2 - (3/2)^2`
`int ("d"x)/((x - 1/2)^2 - (3/2)^2) = 1/(2(3/2)) log |(x - 1/2 - 3/2)/(x - 1/2 + 3/2)| + "c"`
= `1/3log |(x - 2)/(x + 1)| + "c"`
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