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BITSAT2019MathematicsIndefinite IntegrationActual

The integral ∫ 1 + x - 1 x e x + 1 x d x is equal to

Options

  1. Ax - 1 e x + 1 x + C
  2. Bx e x + 1 x + C
  3. Cx + 1 e x + 1 x + C
  4. D- x e x + 1 x + C

Correct answer

B. x e x + 1 x + C

Step-by-step solution

We have, I = ∫ 1 + x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x 1 - 1 x 2 e x + 1 x d x I = ∫ e x + 1 x d x + x e x + 1 x - ∫ e x + 1 x d x I = x e x + 1 x + C

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