Evaluate : x -1 x x +1 dx
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Evaluate : \(\int \frac{\sqrt{\mathrm{x}-1}}{\mathrm{x} \sqrt{\mathrm{x}+1}} \mathrm{dx}\)
- \(\ln \left(\mathrm{x}+\sqrt{\mathrm{x}^{2}+1}\right)+\sec ^{-1} \mathrm{x}+\mathrm{c}\)
- \(\ln \left(\mathrm{x}-\sqrt{\mathrm{x}^{2}+1}\right)-\sec ^{-1} \mathrm{x}+\mathrm{c}\)
- \(\ln \left(\mathrm{x}+\sqrt{\mathrm{x}^{2}-1}\right)-\sec ^{-1} \mathrm{x}+\mathrm{c}\)
- None of these
Answer
(C) ( x + x ^ 2 -1 )- ^ -1 x + c
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