What is the integral from-1 to 5 of-x^2+4x+5-x+1 ?

The integral from-1 to 5 of-x^2+4x+5-x+1 is 30

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integral from-1 to 5 of-x^2+4x+5-x+1

\int_{- 1}^{5} - x^{2} + 4 x + 5 - x + 1 d x

30

Solution steps

\int_{- 1}^{5} - x^{2} + 4 x + 5 - x + 1 d x

Simplify

= \int_{- 1}^{5} - x^{2} + 3 x + 6 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 1}^{5} x^{2} d x + \int_{- 1}^{5} 3 x d x + \int_{- 1}^{5} 6 d x

\int_{- 1}^{5} x^{2} d x = 42

\int_{- 1}^{5} 3 x d x = 36

\int_{- 1}^{5} 6 d x = 36

= - 42 + 36 + 36

Simplify

= 30

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What is the integral from-1 to 5 of-x^2+4x+5-x+1 ?
The integral from-1 to 5 of-x^2+4x+5-x+1 is 30