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Question
`int (xdx)/((x - 1)(x - 2))` equals:
Options
`log |(x - 1)^2/(x - 2)| + C`
`log |(x - 2)^2/(x - 1)| + C`
`log |((x - 1^2)/(x - 2))| + C`
log|(x - 1)(x - 2) + C
Solution
`log abs ((x - 2)^2/(x - 1)) + C`
Explanation:
Let `I = int x/ ((x - 1) (x - 2)) dx`
`= int [(-1)/ (x - 1) + 2/ (x - 2)] dx`
= - log (x - 1) + 2 log (x - 2) + C
`= log |(x - 2)^2/(x - 1)| + C`
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