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Question
Integrate the following with respect to x.
`"e"^(2x)/("e"^(2x) - 2)`
Solution
Let f(x) = e2x – 2
Then f'(x) = 2e2x
So `int "e"^(2x)/("e"^(2x) - 2) "d"x = 1/2 int (2"e"^(2x))/("e"^(2x) - 2) "d"x`
= `1/2 int ("f'"(x))/("f"(x)) "d"x`
= `1/2 log|"f"(x)| + "c"`
= `1/2 log|"e"^(2x) - 2| + "c"`
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