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Question
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
Solution
Let I = `"e"^(3"x")/("e"^(3"x") + 1)` dx
Put e3x + 1 = t
Diff. both the sides w.r.t. x
3 e3x = dt ⇒ e3x dx = `"dt"/3`
`therefore "I" = 1/3 int "dt"/"t"`
`= 1/3 "log" |"t"| + "c"`
`= 1/3 "log" |e^(3x) + 1| + "C"`
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