What is the integral from 1 to 5 of x^3-5x^2-x+5 ?

The integral from 1 to 5 of x^3-5x^2-x+5 is -128/3

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integral from 1 to 5 of x^3-5x^2-x+5

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

- \frac{128}{3}

Decimal

- 42.66666 \dots

Solution steps

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

\int_{1}^{5} x^{3} d x = 156

\int_{1}^{5} 5 x^{2} d x = \frac{620}{3}

\int_{1}^{5} x d x = 12

\int_{1}^{5} 5 d x = 20

= 156 - \frac{620}{3} - 12 + 20

Simplify

156 - \frac{620}{3} - 12 + 20 : - \frac{128}{3}

= - \frac{128}{3}

What is the integral from 1 to 5 of x^3-5x^2-x+5 ?
The integral from 1 to 5 of x^3-5x^2-x+5 is -128/3