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The value of the integral ∫ s i n 2 x s e c 2 x + 2 1 - x 2 t a n x s i n - 1 x 1 - x 2 1 + t a n 2 x d x is (where, C is the constant of integration)

Options

  1. As i n - 1 x c o s 2 x + C
  2. Bs i n - 1 x s i n 2 x + C
  3. Cc o s - 1 x s i n 2 x + C
  4. D- s i n - 1 x s i n 2 x + C

Correct answer

B. s i n - 1 x s i n 2 x + C

Step-by-step solution

∫ s i n 2 x 1 - x 2 + 2 t a n x 1 + t a n 2 x s i n - 1 x d x = ∫ s i n 2 x 1 - x 2 + sin ⁡ 2 x sin - 1 x d x = sin 2 ⁡ x s i n - 1 x + C

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