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Question
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Solution
Let I = `int 1/(1 + "e"^"x")`dx
Dividing Nr. and Dr. by ex, we get
I = `int "e"^-"x"/("e"^-"x" + 1)` dx
Put `"e"^-"x" + 1` = t
∴ `- "e"^-"x" "dx" = "dt"`
∴ `"e"^-"x" "dx" = - "dt"`
∴ I = `int (- "dt")/"t" = - log |"t"| + "c"`
∴ I = - log `|"e"^-"x" + 1|` + c
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