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