x^ 2 -1 (x^ 4 +3 x^ 2 +1 ) ^ -1 ( x^ 2 +1 x ) d x is equal to
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\[\int \frac{x^{2}-1}{\left(x^{4}+3 x^{2}+1\right) \tan ^{-1}\left(\frac{x^{2}+1}{x}\right)} d x\] is equal to
- \(\tan ^{-1}\left(x+\frac{1}{x}\right)+c\)
- \(\log _{e}\left|\tan ^{-1}\left(x+\frac{1}{x}\right)\right|+c\)
- \(\log _{e}\left|\tan \left(\frac{x^{2}+1}{x}\right)\right|+c\)
- \(\left(x+\frac{1}{x}\right) \tan ^{-1}\left(x+\frac{1}{x}\right)+c\)
Answer
(B) _ e | ^ -1 (x+ 1 x ) |+c
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