What is the integral from 0 to 5 of (x^2+x+1) ?

The integral from 0 to 5 of (x^2+x+1) is 355/6

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integral from 0 to 5 of (x^2+x+1)

\int_{0}^{5} (x^{2} + x + 1) d x

\frac{355}{6}

Decimal Notation

59.16666 \dots

Solution steps

\int_{0}^{5} x^{2} + x + 1 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_{0}^{5} x^{2} d x + \int_{0}^{5} x d x + \int_{0}^{5} 1 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} x d x = \frac{25}{2}

\int_{0}^{5} 1 d x = 5

= \frac{125}{3} + \frac{25}{2} + 5

Simplify

\frac{125}{3} + \frac{25}{2} + 5 : \frac{355}{6}

= \frac{355}{6}

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What is the integral from 0 to 5 of (x^2+x+1) ?
The integral from 0 to 5 of (x^2+x+1) is 355/6