If ( 1- x 1+ x )^ 1 / 2 d x x =2 ^ -1 x -f(x)+c then f (x) equals.
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \[\int\left(\frac{1-\sqrt{x}}{1+\sqrt{x}}\right)^{1 / 2} \frac{d x}{x}=2 \cos ^{-1} \sqrt{x}-f(x)+c\]then f (x) equals.
- \(\log _{e}\left(\frac{1+\sqrt{1-x}}{\sqrt{x}}\right)\)
- \(\frac{1}{2} \log _{e}\left(\frac{1+\sqrt{1-x}}{\sqrt{x}}\right)\)
- \(2 \log _{e}\left(\frac{1-\sqrt{1-x}}{\sqrt{x}}\right)\)
- \(2 \log _{e}\left(\frac{1+\sqrt{1-x}}{\sqrt{x}}\right)\)
Answer
(D) 2 _ e ( 1+ 1-x x )
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