The value of \int {1}/{x+\sqrt{x-1}} \dx is

Correct Answer is : log(x+√x−1)−2√3tan−1(2√x−1+1√3)+C

\log (x+\sqrt{x-1})+ \sin ^{-1} (\sqrt{\frac{x-1}{x}}) +C

\log (x+\sqrt{x-1})- {2}/{\sqrt{3}} \tan ^{-1} ( {2 \sqrt{x-1}+1}/{\sqrt{3}}) +C

\log (x-1+\sqrt{x-1})+ {1}/{\sqrt{3}} \log {| {x-2-\sqrt{3}}/{x-2+\sqrt{3}} |}+C

COMEDK 2024 Shift 1 Paper

Question : 119 of 180

Marks: +1, -0

The value of ∫‌

x+√x−1

‌dx is

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