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If ∫ x x + 1 + e x d x = p x + q ln ⁡ x + 1 + e x + c , where c is the constant of integration, then p + q is equal to

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

∫ x + 1 + e x - e x + 1 x + 1 + e x d x = ∫ 1 - e x + 1 x + 1 + e x d x = x - ln ⁡ x + 1 + e x + c On comparing, p = 1 ,   q = - 1 Hence, p + q = 0

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