What is the integral from 1 to 5 of (x^2+4x+5) ?

The integral from 1 to 5 of (x^2+4x+5) is 328/3

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integral from 1 to 5 of (x^2+4x+5)

\int_{1}^{5} (x^{2} + 4 x + 5) d x

\frac{328}{3}

Decimal

109.33333 \dots

Solution steps

\int_{1}^{5} x^{2} + 4 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^{2} d x + \int_{1}^{5} 4 x d x + \int_{1}^{5} 5 d x

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

\int_{1}^{5} 4 x d x = 48

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

= \frac{124}{3} + 48 + 20

Simplify

\frac{124}{3} + 48 + 20 : \frac{328}{3}

= \frac{328}{3}

What is the integral from 1 to 5 of (x^2+4x+5) ?
The integral from 1 to 5 of (x^2+4x+5) is 328/3