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Consider the integrals I 1 = ∫ e x 2 cos ⁡ x d x and I 2 = ∫ x e x 2 sin ⁡ x d x . Then, I 1 + 2 I 2 simplifies to (where, c is the constant of integration)

Options

  1. Ae x sin ⁡ x + c
  2. Be x 2 cos ⁡ x + c
  3. C2 e x 2 sin ⁡ x + c
  4. De x 2 sin ⁡ x + c

Correct answer

D. e x 2 sin ⁡ x + c

Step-by-step solution

I 1 + 2 I 2 = ∫ e x 2 cos ⁡ x + 2 x e x 2 sin ⁡ x d x = ∫ d e x 2 sin ⁡ x = e x 2 sin ⁡ x + c

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