Evaluate d x (1+x^ 2 ) 1-x^ 2
Mathematics · JEE Main · NTA Exams — Integral Calculus
Evaluate \[\int \frac{d x}{\left(1+x^{2}\right) \sqrt{1-x^{2}}}\]
- \(-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^{2}}}\right)+c\)
- \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} \mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}\right)+\mathrm{c}\)
- \[-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{\sqrt{2} x}\right)+c\]
- \[\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{\sqrt{2} x}\right)+c\]
Answer
(C) - 1 2 ^ -1 ( 1-x^ 2 2 x )+c
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