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

The integral from-1 to 3 of (x^2+3)^3 is 38912/35

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

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

\frac{38912}{35}

Decimal

1111.77142 \dots

Solution steps

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

Expand

(x^{2} + 3)^{3} : x^{6} + 9 x^{4} + 27 x^{2} + 27

= \int_{- 1}^{3} x^{6} + 9 x^{4} + 27 x^{2} + 27 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}^{3} x^{6} d x + \int_{- 1}^{3} 9 x^{4} d x + \int_{- 1}^{3} 27 x^{2} d x + \int_{- 1}^{3} 27 d x

\int_{- 1}^{3} x^{6} d x = \frac{2188}{7}

\int_{- 1}^{3} 9 x^{4} d x = \frac{2196}{5}

\int_{- 1}^{3} 27 x^{2} d x = 252

\int_{- 1}^{3} 27 d x = 108

= \frac{2188}{7} + \frac{2196}{5} + 252 + 108

Simplify

\frac{2188}{7} + \frac{2196}{5} + 252 + 108 : \frac{38912}{35}

= \frac{38912}{35}

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What is the integral from-1 to 3 of (x^2+3)^3 ?
The integral from-1 to 3 of (x^2+3)^3 is 38912/35