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Question Number 163638 by mkam last updated on 08/Jan/22

$$\int \frac{\mathit{d}\mathit{x}}{\sqrt{2{\mathit{c}}_1+{\mathit{e}}^{-2\mathit{x}}}}$$

Commented by mkam last updated on 09/Jan/22

$$?????$$

Commented by mr W last updated on 09/Jan/22

$$fora>0:$$$$\int \frac{dx}{\sqrt{a+e^{-x}}}=\frac{1}{\sqrt{a}}\ln \mid \frac{\sqrt{a+e^{-x}}+\sqrt{a}}{\sqrt{a+e^{-x}}-\sqrt{a}}\mid +C$$$$fora<0:$$$$\int \frac{dx}{\sqrt{a+e^{-x}}}=-\frac{2}{\sqrt{-a}}{\tan }^{-1}\frac{\sqrt{a+e^{-x}}}{\sqrt{-a}}+C$$

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