What is the integral from 0 to 2 of x(x^2+3)^2 ?

The integral from 0 to 2 of x(x^2+3)^2 is 158/3

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integral from 0 to 2 of x(x^2+3)^2

\int_{0}^{2} x (x^{2} + 3)^{2} d x

\frac{158}{3}

Decimal Notation

52.66666 \dots

Solution steps

\int_{0}^{2} x (x^{2} + 3)^{2} d x

Expand

x (x^{2} + 3)^{2} : x^{5} + 6 x^{3} + 9 x

= \int_{0}^{2} x^{5} + 6 x^{3} + 9 x 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}^{2} x^{5} d x + \int_{0}^{2} 6 x^{3} d x + \int_{0}^{2} 9 x d x

\int_{0}^{2} x^{5} d x = \frac{32}{3}

\int_{0}^{2} 6 x^{3} d x = 24

\int_{0}^{2} 9 x d x = 18

= \frac{32}{3} + 24 + 18

Simplify

\frac{32}{3} + 24 + 18 : \frac{158}{3}

= \frac{158}{3}

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What is the integral from 0 to 2 of x(x^2+3)^2 ?
The integral from 0 to 2 of x(x^2+3)^2 is 158/3