What is the integral from 0 to 2 of (x^4+5)^3 ?

The integral from 0 to 2 of (x^4+5)^3 is 86326/39

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integral from 0 to 2 of (x^4+5)^3

\int_{0}^{2} (x^{4} + 5)^{3} d x

\frac{86326}{39}

Decimal

2213.48717 \dots

Solution steps

\int_{0}^{2} (x^{4} + 5)^{3} d x

Expand

(x^{4} + 5)^{3} : x^{12} + 15 x^{8} + 75 x^{4} + 125

= \int_{0}^{2} x^{12} + 15 x^{8} + 75 x^{4} + 125 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^{12} d x + \int_{0}^{2} 15 x^{8} d x + \int_{0}^{2} 75 x^{4} d x + \int_{0}^{2} 125 d x

\int_{0}^{2} x^{12} d x = \frac{8192}{13}

\int_{0}^{2} 15 x^{8} d x = \frac{2560}{3}

\int_{0}^{2} 75 x^{4} d x = 480

\int_{0}^{2} 125 d x = 250

= \frac{8192}{13} + \frac{2560}{3} + 480 + 250

Simplify

\frac{8192}{13} + \frac{2560}{3} + 480 + 250 : \frac{86326}{39}

= \frac{86326}{39}

What is the integral from 0 to 2 of (x^4+5)^3 ?
The integral from 0 to 2 of (x^4+5)^3 is 86326/39