dx-e-2x-4-sec-1-e-x-4-

Question Number 76467 by kaivan.ahmadi last updated on 27/Dec/19

\int \frac{d x}{\sqrt{e^{2 x} - 4} ({s e c}^{- 1} (\frac{e^{x}}{4}))}

Answered by john santu last updated on 28/Dec/19

l e t : \sec u = \frac{e^{x}}{4} \to e^{x} d x = 4 \sec u \times \tan u d u

I = \int \frac{4 \sec u \times \tan u d u}{e^{x} (\sqrt{e^{2 x} - 4})}

= \int \frac{4 \sec u . \tan u d u}{4 \sec u \sqrt{16 \sec^{2} u - 4}}

\int \frac{\tan u d u}{2 \sqrt{4 \sec^{2} u - 1}} = \int \frac{\tan u d u}{2 \sqrt{4 \tan^{2} u + 3}}

n o w l e t \tan u = β

Commented by kaivan.ahmadi last updated on 29/Dec/19

t h a n k y o u s i r