Question

How do you integrate `int e^(2x)/sqrt(-e^(2x) -81)dx` using trigonometric substitution?

Answer 1

See the Explanation below.

Explanation:

I doubt that this integration is possible in `RR`.

This is because, `AA x in RR, e^(2x)>0, 81>0 rArr (e^(2x)+81)>0`

`rArr -(e^(2x)+81)=-e^(2x)-81<0`

`rArr {sqrt(-e^(2x)-81)} "is undefined"`