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COMEDK2020MathematicsIndefinite Integration

The value of e^ x (x⁵+5 x⁴+1 ) d x is

Options

  1. Ae^ x x⁵+e^ x +C
  2. Be^ x x⁵
  3. C5 x⁴ e^ x
  4. De^ x+1 x⁵+C

Correct answer

A. e^ x x⁵+e^ x +C

Step-by-step solution

Let aligned &I= e^ x (x⁵+5 x⁴+1 ) d x &= e_ I I ^ x (x⁵+1 ) d x+ e^ x (5 x⁴ ) d x aligned = (x⁵+1 ) e^ x d x- [ ( e^ x d x ) d d x x⁵+1 ) ] d x + e^ x (5 x⁴ ) d x = x⁵+1 ) e^ x - e^ x (5 x⁴ ) d x+ e^ x (5 x⁴ ) d x = (x⁵+1 ) e^ x +C=e^ x x⁵+e^ * +C

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