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COMEDK2018MathematicsIndefinite Integration

e^ x 1+ x x ² x d x=

Options

  1. Ae^ x x+c
  2. Be^ x x x+c
  3. Ce^ x x+c
  4. De^ x ² x-1+c

Correct answer

C. e^ x x+c

Step-by-step solution

We have, aligned & e^ x 1+ x x ² x d x &= e^ x 1 ² x + x x ² x d x &= e^ x ( ²+ x ) d x= e^ x f^ (x)+f(x) d x & [ where f(x)= x and f^ (x)= ² x ] &=e^ x f(x)+c=e^ x x+c aligned

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