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Question
Evaluate `int 1/("x" ("x" - 1))` dx
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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