\( \int \frac{d x}{\sqrt{2 e^{x}-1}}= \) \( \mathrm{P} \) (1) \( 2 ...

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\( \int \frac{d x}{\sqrt{2 e^{x}-1}}= \)
\( \mathrm{P} \)
(1) \( 2 \sec ^{-1} \sqrt{2 e^{x}}+c \)
(2) \( -2 \tan ^{-1} \frac{1}{\sqrt{2 e^{x}-1}}+c \)
(3) \( 2 \sec ^{-1}\left(\sqrt{2} e^{x}\right)+c \)
(4) \( 2 \tan ^{-1} \sqrt{2 e^{x}-1}+c \)
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