Evaluate : 1+x^ 2 n x^ 2 n (1+x^ 2 n )-2 n / n x x^ 2 n+1 d x

Mathematics · JEE Advanced · NTA Exams — Integral Calculus

1. \(\frac{2 \mathrm{P}^{3}}{9 \mathrm{n}}(1-3 \ln \mathrm{P})+\mathrm{C}\)
2. \(\frac{\mathrm{P}^{3}}{3 \mathrm{n}}(3 \ln \mathrm{P}-1)+\mathrm{C}\)
3. \(\frac{2 \mathrm{P}^{3}}{3 \mathrm{n}}(3 \ln \mathrm{P}-1)+\mathrm{C}\)
4. None of these
   \(\text { where } P=\left(1+\frac{1}{x^{2 n}}\right)^{1 / 2}\)

Answer

(A) 2 P ^ 3 9 n (1-3 P )+ C

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