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

Question

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, 0, 1, 2, 3

MARKS App · Accepted Answer

∫ 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