1.

\[\int \frac{\sqrt{x-1}}{x\sqrt{x+1}}dx\]is equal to

A. \[\ln \,\left| x-\sqrt{{{x}^{2}}-1} \right|-{{\tan }^{-1}}x+c\]
B. \[\ln \,\left| x+\sqrt{{{x}^{2}}-1} \right|-{{\tan }^{-1}}x+c\]
C. \[\ln \,\left| x-\sqrt{{{x}^{2}}-1} \right|-{{\sec }^{-1}}x+c\]
D. \[\ln \,\left| x+\sqrt{{{x}^{2}}-1} \right|-{{\sec }^{-1}}x+c\]
Answer» E.


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