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MHT CET202124 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual

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

Options

  1. A1 e ^ 2 x +1 + c
  2. B-1 e ^ x +1 + c
  3. C1 e ^ x + c
  4. D-1 e ^ x + c

Correct answer

B. -1 e ^ x +1 + c

Step-by-step solution

Let aligned I & = d x e^x+e^ -x +2 & = d x e^x+ 1 e^x +2 = e^x d x e^ 2 x +2 e^x+1 = e^x (e^x+1 )^2 d x aligned Put e ^ x +1= t e ^ x dx = dt I= d t t^2 = t^2 d t= t⁻¹ -1 +c= -1 t +c= -1 e^x+1 +c

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