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COMEDK2014MathematicsIndefinite Integration

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

Options

  1. Ae^ x x+C
  2. Be^ x x+C
  3. C-e^ x x+C
  4. D-e^ x x+C

Correct answer

A. e^ x x+C

Step-by-step solution

aligned Let I &= e^ x ( x- x) d x &= e^ x x d x- e^ x x d x &= e^ x x d x- [e^ x (- x)- e^ x (- x) d x ] &= e^ x x d x+e^ x x- e^ x x d x &=e^ x x+C aligned

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