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Question
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Options
log x – log (1 – x) + c
log (1 - x2) + c
- log x + log(1 - x) + c
log (x - x2) + c
Solution
log x – log (1 – x) + c
Explanation:
Let I = `int "dx"/(("x" - "x"^2))`
`= int 1/("x"(1 - "x"))` dx
`= int ((1 - "x")+"x")/("x"(1 - "x"))` dx
`= int (1/"x" + 1/"1 - x")` dx
`= log |"x"| + (log |1 - "x"|)/-1` + c
= log |x| - log |1 - x| + c
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