1.

\[\int{\sqrt{{{e}^{x}}-1}}dx=\]   [Kerala (Engg.) 2005]

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


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