Question

Integrate the following with respect to x.

`"e"^(2x)/("e"^(2x) - 2)`

Answer 1

Let f(x) = e^2x – 2

Then f'(x) = 2e^2x 

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"`