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Manipal MET2018MathematicsIndefinite Integration

2 d x (e^x+e^ -x )^2 is equal to

Options

  1. A- e^ -x (e^x+e^ -x ) +c
  2. B- 1 (e^x+e^ -x ) +c
  3. C1 (e^x+1 )^2 +c
  4. D1 (e^x-e^ -x )^2 +c

Correct answer

A. - e^ -x (e^x+e^ -x ) +c

Step-by-step solution

Let aligned I & = 2 d x (e^x+e^ -x )^2 = 2 d x e^ 2 x +e^ -2 x +2 & = 2 e^ 2 x d x e^ 4 x +2 e^ 2 x +1 aligned Put e^ 2 x =t 2 e^ 2 x d x=d t aligned I & = d t t^2+2 t+1 = d t (t+1)^2 =- 1 t+1 +c & =- 1 e^ 2 x +1 =- e^ -x e^x+e^ -x +c aligned

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