Question

Integrate the following with respect to x.

`"e"^x/("e"^(2x) - 9)`

Answer 1

`int ("e"^x "d"x)/("e"^(2x) - 9) = int ("e"^x  "d"x)/(("e"^x)^2 - 3^2)`

Let e^x = t

Then e^x dx = dt

= `int "dt"/("t"^2 - 3^2)`

= `1/(2(3)) log|("t" - 3)/("t" + 3)| +"c"`

= `1/6 log |("e"^x - 3)/("e"^x + 3)| + "c"`