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MHT CET202415 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

(1+x- 1 x ) e ^ x+ 1 x ~d x is equal to

Options

  1. A(x-1) e ^ x+ 1 x + c , where c is a constant of integration.
  2. Bx e ^ x+ 1 x + c , where c is a constant of integration.
  3. C(x+1) e ^ x+ 1 x + c , where c is a constant of integration.
  4. D-x e ^ x+ 1 x + c , where c is a constant of integration.

Correct answer

B. x e ^ x+ 1 x + c , where c is a constant of integration.

Step-by-step solution

aligned & (1+x-x⁻¹ ) e ^ x+x⁻¹ ~d x & = [x e ^ x+x⁻¹ (1- 1 x^2 )+ e ^ x+x⁻¹ ] d x & =x e ^ x+x⁻¹ + c [ [x f ^ (x)+ f (x) ] d x=x f (x)+ c ] aligned

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