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The integral I = ∫ e e sin ⁡ x + sin ⁡ x cos ⁡ x d x simplifies to (where, c is the constant of integration)

Options

  1. Ae sin ⁡ x + c
  2. Be sin ⁡ x + cos ⁡ x + c
  3. Ce e cos ⁡ x + c
  4. De e sin ⁡ x + c

Correct answer

D. e e sin ⁡ x + c

Step-by-step solution

The given integral is I = ∫ e e sin ⁡ x e sin ⁡ x cos ⁡ x d x Let e e sin ⁡ x = t ⇒ e e sin ⁡ x e sin ⁡ x cos ⁡ x d x = d t ∴ I = ∫ 1 d t = t + c ⇒ I = e e sin ⁡ x + c

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