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VITEEE2013MathematicsDefinite Integration

(1+x-x⁻¹ ) e^ x+x⁻¹ d x is equal to

Options

  1. A(x+1) e ^ x+x⁻¹ +C
  2. B(x-1) e ^ x+x⁻¹ +C
  3. Cx e^ x+x⁻¹ +C
  4. Dx e^ x+x⁻¹ x+C

Correct answer

C. x e^ x+x⁻¹ +C

Step-by-step solution

(1+x-x⁻¹ ) e^ x+x⁻¹ d x= [x e^ x+x⁻¹ (1- 1 x² )+e^ x+x⁻¹ ] d x [ x f^ (x)+f(x) d x=x f(x)+C ] (1+x-x⁻¹ ) e^ x+x⁻¹ d x=x e^ x+x⁻¹ +C

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