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

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Answer 1 · 2016-08-24T15:43:01

See the Explanation below.

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

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

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

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

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