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

\int_{0}^{\frac{π}{3}} (1 - 2 sin (x))^{2} d x

\int_{0}^{3} 1 + (8 x)^{2} d x

\int_{1}^{2} x (2 - x) (x - 1) d x

\int_{3}^{5} \frac{5}{( x - 4 ) ^{2}} d x

\int_{1}^{3} x e^{3 x} d x

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