\( \int \frac{a^{x / 2}}{\sqrt{a^{-x}-a^{x}}} d x= \) (A) \( \frac{1}{\log a} \sin ^{-1}\left(a^...
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0\( \int \frac{a^{x / 2}}{\sqrt{a^{-x}-a^{x}}} d x= \)
(A) \( \frac{1}{\log a} \sin ^{-1}\left(a^{x}\right) \)
(B) \( \frac{1}{\log a} \tan ^{-1}\left(a^{x}\right) \)
(C) \( 2 \sqrt{a^{-x}-a^{x}} \)
(D) \( \log \left(a^{x}-1\right) \)
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