What is the integral from 2 to 5 of (x^3+3x^2+5x+9) ?

The integral from 2 to 5 of (x^3+3x^2+5x+9) is 1395/4

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integral from 2 to 5 of (x^3+3x^2+5x+9)

\int_{2}^{5} (x^{3} + 3 x^{2} + 5 x + 9) d x

\frac{1395}{4}

Decimal

348.75

Solution steps

\int_{2}^{5} x^{3} + 3 x^{2} + 5 x + 9 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_{2}^{5} x^{3} d x + \int_{2}^{5} 3 x^{2} d x + \int_{2}^{5} 5 x d x + \int_{2}^{5} 9 d x

\int_{2}^{5} x^{3} d x = \frac{609}{4}

\int_{2}^{5} 3 x^{2} d x = 117

\int_{2}^{5} 5 x d x = \frac{105}{2}

\int_{2}^{5} 9 d x = 27

= \frac{609}{4} + 117 + \frac{105}{2} + 27

Simplify

\frac{609}{4} + 117 + \frac{105}{2} + 27 : \frac{1395}{4}

= \frac{1395}{4}

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What is the integral from 2 to 5 of (x^3+3x^2+5x+9) ?
The integral from 2 to 5 of (x^3+3x^2+5x+9) is 1395/4