What is the integral of 5/(\sqrt[3]{x)} ?

The integral of 5/(\sqrt[3]{x)} is 15/2 x^{2/3}+C

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integral of 5/(\sqrt[3]{x)}

\frac{15}{2} x^{\frac{2}{3}} + C

Solution steps

Take the constant out:

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

Apply the Power Rule

: \frac{3}{2} x^{\frac{2}{3}}

= 5 \cdot \frac{3}{2} x^{\frac{2}{3}}

Simplify

5 \cdot \frac{3}{2} x^{\frac{2}{3}} : \frac{15}{2} x^{\frac{2}{3}}

= \frac{15}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{15}{2} x^{\frac{2}{3}} + C

\frac{d}{d x} (\frac{arcsin ( x )}{1 - x ^{2}})

x \to 8 - lim (\frac{64 - x ^{2}}{x - 8})

\frac{d}{d x} (x 64 - x^{2})

What is the integral of 5/(\sqrt[3]{x)} ?
The integral of 5/(\sqrt[3]{x)} is 15/2 x^{2/3}+C