(x^ 2 -1 ) d x 2 x x^ 4 +4 x^ 3 -6 x^ 2 +4 x+1 is
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\(\int \frac{\left(x^{2}-1\right) d x}{2 x \sqrt{x^{4}+4 x^{3}-6 x^{2}+4 x+1}} \text { is }\)
- \[\frac{1}{2} \ln \left|\mathrm{x}+\frac{1}{\mathrm{x}}+2+\sqrt{\left(\mathrm{x}+\frac{1}{\mathrm{x}}+2\right)^{2}-12}\right|+\mathrm{c}\]
- \[\frac{1}{2} \ln \left|\mathrm{x}-\frac{1}{\mathrm{x}}+2+\sqrt{\left(\mathrm{x}-\frac{1}{\mathrm{x}}+2\right)^{2}-12}\right|+\mathrm{c}\]
- \[\frac{1}{2} \ln \left|\mathrm{x}+\frac{1}{\mathrm{x}}-2+\sqrt{\left(\mathrm{x}+\frac{1}{\mathrm{x}}-2\right)^{2}-12}\right|+\mathrm{c}\]
- None of these
Answer
(A) 1 2 | x + 1 x +2+ ( x + 1 x +2 )^ 2 -12 |+ c
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