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MHT CET202016 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual

1+2 e^ -x 1-2 e^ -x d x=

Options

  1. Ax- (1-2 e^ -x )+ c
  2. B(1-2 e^ -x )+ c
  3. Cx+ (1-2 e^ -x )+ c
  4. Dx+2 (1-2 e^ -x )+ c

Correct answer

D. x+2 (1-2 e^ -x )+ c

Step-by-step solution

(B) Let aligned 1 &= 1-2 e^ -x 1-2 e⁻¹ =& 1-2 e^ -x +4 e^ -x 1-2 e⁻¹ d x= 1-2 e^ -x 1-2 e⁻¹ d x+4 e^ -x 1-2 e^ -x d x =& d x+ 4 2 2 e^ -x 1-2 e^ -x d x=x-2 1-2 e⁻¹-c aligned

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