What is the integral from-1 to 2 of x^2(x^3+2)^2 ?

The integral from-1 to 2 of x^2(x^3+2)^2 is 111

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integral from-1 to 2 of x^2(x^3+2)^2

\int_{- 1}^{2} x^{2} (x^{3} + 2)^{2} d x

111

Solution steps

\int_{- 1}^{2} x^{2} (x^{3} + 2)^{2} d x

Expand

x^{2} (x^{3} + 2)^{2} : x^{8} + 4 x^{5} + 4 x^{2}

= \int_{- 1}^{2} x^{8} + 4 x^{5} + 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_{- 1}^{2} x^{8} d x + \int_{- 1}^{2} 4 x^{5} d x + \int_{- 1}^{2} 4 x^{2} d x

\int_{- 1}^{2} x^{8} d x = 57

\int_{- 1}^{2} 4 x^{5} d x = 42

\int_{- 1}^{2} 4 x^{2} d x = 12

= 57 + 42 + 12

Simplify

= 111

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What is the integral from-1 to 2 of x^2(x^3+2)^2 ?
The integral from-1 to 2 of x^2(x^3+2)^2 is 111