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The value of ∫ - 1 1 sin - 1 ⁡ x + x 5 + x 3 - 1 cos 2 ⁡ x d x is equal to

Options

  1. Atan ⁡ 1
  2. B0
  3. C2 tan ⁡ 1
  4. D- 2 tan ⁡ 1

Correct answer

D. - 2 tan ⁡ 1

Step-by-step solution

Let, I = ∫ - 1 1 sin - 1 ⁡ x + x 5 + x 3 - 1 cos 2 ⁡ x d x I = ∫ - 1 1 - 1 cos 2 ⁡ x ⁡ d x I = - ∫ - 1 1 sec 2 ⁡ x d x I = - tan ⁡ x - 1 1 I = - 2 tan ⁡ 1

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