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The integral I = ∫ 1 x ⋅ sec ⁡ x - ln ⁡ x sin ⁡ x d x simplifies to (where, c is the constant of integration)

Options

  1. Aln ⁡ x sin ⁡ x + c
  2. Bln ⁡ x cos ⁡ x + c
  3. Cx ln ⁡ sin ⁡ x + c
  4. Dx ln ⁡ cos ⁡ x + c

Correct answer

B. ln ⁡ x cos ⁡ x + c

Step-by-step solution

Given I = ∫ cos ⁡ x ⋅ 1 x + - sin ⁡ x ln ⁡ x d x Since, ∫ f ⋅ g ' + f ' g d x = f ⋅ g + c ⇒ I = cos ⁡ x ln ⁡ x + c

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