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Question
Evaluate `int 1/(x (x - 1))` dx
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Solution
Let I = `int 1/(x (x - 1))` dx
`= int (x - x + 1)/(x(x - 1))` dx
`= int (x - (x - 1))/(x(x - 1))` dx
`= int (1/(x - 1) - 1/x)` dx
`= int 1/(x - 1) dx - int 1/x dx`
`= log |x - 1| - log |x| + c`
∴ I = log `|(x - 1)/x| + c`
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