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

The integral from 1 to 5 of (x^2+2x+3) is 232/3

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integral from 1 to 5 of (x^2+2x+3)

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

\frac{232}{3}

Decimal Notation

77.33333 \dots

Solution steps

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

\int_{1}^{5} x^{2} d x = \frac{124}{3}

\int_{1}^{5} 2 x d x = 24

\int_{1}^{5} 3 d x = 12

= \frac{124}{3} + 24 + 12

Simplify

\frac{124}{3} + 24 + 12 : \frac{232}{3}

= \frac{232}{3}

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What is the integral from 1 to 5 of (x^2+2x+3) ?
The integral from 1 to 5 of (x^2+2x+3) is 232/3