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

The integral from-2 to 2 of x^2(x^2+1) is 272/15

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

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

\frac{272}{15}

Decimal Notation

18.13333 \dots

Solution steps

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

Expand

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

= \int_{- 2}^{2} x^{4} + x^{2} 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}^{2} x^{4} d x + \int_{- 2}^{2} x^{2} d x

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= \frac{64}{5} + \frac{16}{3}

Simplify

\frac{64}{5} + \frac{16}{3} : \frac{272}{15}

= \frac{272}{15}

x = 0, y = (3 x + 1)^{\frac{1}{4}}, [0, 8]

x \to 2 - lim (x^{2})

2 x^{2} - 7 x + 5

(x + \frac{4}{x})^{^{'}}

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2} + z^{2})})

What is the integral from-2 to 2 of x^2(x^2+1) ?
The integral from-2 to 2 of x^2(x^2+1) is 272/15