Evaluate \( \int \frac{\sqrt{x-1}}{x \sqrt{x+1}} d x \) (a) \( \ln \left(x+\sqrt{x^{2}-1}\right)...

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Evaluate \( \int \frac{\sqrt{x-1}}{x \sqrt{x+1}} d x \)
(a) \( \ln \left(x+\sqrt{x^{2}-1}\right)+\tan ^{-1} x+c \)
(b) \( \ln \left(x+\sqrt{x^{2}-1}\right)+\sec ^{-1} x \)
(c) \( \ln \left(x+\sqrt{x^{2}-1}\right)-\sec ^{-1} x+c \)
(d) \( \ln \left(x+\sqrt{x^{2}-1}\right)-\tan ^{-1} x+c \)
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