What is the integral from 0 to 8 of (1+\sqrt[3]{x}) ?

The integral from 0 to 8 of (1+\sqrt[3]{x}) is 20

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integral from 0 to 8 of (1+\sqrt[3]{x})

\int_{0}^{8} (1 + 3 x) d x

20

Solution steps

\int_{0}^{8} 1 + 3 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}^{8} 1 d x + \int_{0}^{8} 3 x d x

\int_{0}^{8} 1 d x = 8

\int_{0}^{8} 3 x d x = 12

= 8 + 12

Simplify

= 20

\int e^{\frac{3}{x}} d x

\frac{s - 6}{3 s ^{2} + s + 12}

\int e^{\frac{x}{2} + 3} d x

\int \frac{2 y - 1}{y} d y

f (x) = e^{5}

What is the integral from 0 to 8 of (1+\sqrt[3]{x}) ?
The integral from 0 to 8 of (1+\sqrt[3]{x}) is 20