How do you integrate $int 1/sqrt(-e^(2x) +100)dx$ using trigonometric substitution?

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Answer 1 · 2016-07-10T19:36:06

$1/10 int (dy)/cosy$

Making $e^{-x} = 10 cosy$ we have

$- e^{-x}dx = -10 sin y dy$

and

$dx = 10 siny/e^{-x}dy = tan y dy$

so

$int (dx)/sqrt(-e^(2x) +100) equiv 1/10int (tany)/sinydy = 1/10 int (dy)/cosy$

How do you integrate int 1/sqrt(-e^(2x) +100)dxint 1/sqrt(-e^(2x) +100)dx using trigonometric substitution?