0-1-e-x-1-dx-

Question Number 151761 by talminator2856791 last updated on 22/Aug/21

\int_{0}^{\infty} \frac{1}{\sqrt{e^{x} + 1}} d x

Answered by mindispower last updated on 22/Aug/21

\int_{0}^{\infty} \frac{e^{- \frac{x}{2}} d x}{\sqrt{1 + {(e^{- \frac{x}{2}})}^{2}}} = - 2 \int_{0}^{\infty} \frac{{d e}^{- \frac{x}{2}}}{\sqrt{1 + {(e^{- \frac{x}{2}})}^{2}}}

= - 2 {[a r g s h (e^{- \frac{x}{2}})]}_{0}^{\infty}

= 2 a r g s h (1) = l n (3 + 2 \sqrt{2})