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JEE Main20205 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual

If ∫ e 2 x + 2 e x - e - x - 1 e e x + e - x d x = g ( x ) e e x + e - x + c , where c is a constant of integration, then g ( 0 ) is

Options

  1. Ae
  2. Be 2
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

I = ∫ e 2 x + 2 e x - e - x - 1 e e x + e - x d x ⇒ I = ∫ e 2 x + e x - 1 e e x + e - x d x + ∫ e x - e - x e e x + e - x d x ⇒ I = ∫ e x + 1 - e - x e e x + e - x + x d x + e e x + e - x + c e x + e - x + x = u e x - e - x + 1 d x = d u I = e e x + e - x + x + e e x + e - x + c = e e x + e - x e x + 1 + c then g ( x ) = e x + 1 g ( 0 ) = 2

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