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KCET2007MathematicsIndefinite Integration

The value of e^ x (x⁵+5 x⁴+1 ) d x is

Options

  1. Ae^ x x⁵+c
  2. Be^ x x⁵+e^ x +c
  3. Ce^ x+1 x⁵+c
  4. D5 x⁴ e^ x +c

Correct answer

B. e^ x x⁵+e^ x +c

Step-by-step solution

Let I= e^ x (x⁵+5 x⁴+1 ) d x aligned &= e^ x x⁵ d x+5 e^ x x⁴ d x+ e^ x d x &=x⁵ e^ x - 5 x⁴ e^ x d x+5 e^ x x⁴ d x+e^ x &=x⁵ e^ x +e^ x +c aligned

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