What is the integral from 0 to 8 of 5/(x^{2/3)} ?

The integral from 0 to 8 of 5/(x^{2/3)} is 30

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integral from 0 to 8 of 5/(x^{2/3)}

\int_{0}^{8} \frac{5}{x ^{\frac{2}{3}}} d x

30

Solution steps

\int_{0}^{8} \frac{5}{x ^{\frac{2}{3}}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{8} \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

: [3 x^{\frac{1}{3}}]_{0}^{8}

= 5 [3 x^{\frac{1}{3}}]_{0}^{8}

Compute the boundaries:

6

= 5 \cdot 6

Simplify

= 30

y = 2 x^{2} + 1

\frac{d}{d x} ((cos (3 x))^{x})

f (x) = sin (x) ln (x^{2} + 1)

x \to π lim (9 cot (x))

What is the integral from 0 to 8 of 5/(x^{2/3)} ?
The integral from 0 to 8 of 5/(x^{2/3)} is 30