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

The integral from 1 to 5 of (x^2+1)^2 is 10672/15

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

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

\frac{10672}{15}

Decimal

711.46666 \dots

Solution steps

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

Expand

(x^{2} + 1)^{2} : x^{4} + 2 x^{2} + 1

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

\int_{1}^{5} x^{4} d x = \frac{3124}{5}

\int_{1}^{5} 2 x^{2} d x = \frac{248}{3}

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

= \frac{3124}{5} + \frac{248}{3} + 4

Simplify

\frac{3124}{5} + \frac{248}{3} + 4 : \frac{10672}{15}

= \frac{10672}{15}

What is the integral from 1 to 5 of (x^2+1)^2 ?
The integral from 1 to 5 of (x^2+1)^2 is 10672/15