What is the integral of (\sqrt[3]{x^8}) ?

The integral of (\sqrt[3]{x^8}) is 3/11 x^{11/3}+C

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integral of (\sqrt[3]{x^8})

\int (3 x^{8}) d x

\frac{3}{11} x^{\frac{11}{3}} + C

Solution steps

\int 3 x^{8} d x

3 x^{8} = x^{\frac{8}{3}},

assuming

x \geq 0

= \int x^{\frac{8}{3}} d x

Apply the Power Rule

: \frac{3}{11} x^{\frac{11}{3}}

= \frac{3}{11} x^{\frac{11}{3}}

Add a constant to the solution

= \frac{3}{11} x^{\frac{11}{3}} + C

\int \frac{1}{13 x} d x

\int 9 arctan (\frac{1}{x}) d x

x \to \infty lim (ln (x) + ln (\frac{1}{\frac{1}{x} + 1}))

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

g (u) = \frac{8 u ^{2}}{( u ^{2} + u ) ^{3}}

What is the integral of (\sqrt[3]{x^8}) ?
The integral of (\sqrt[3]{x^8}) is 3/11 x^{11/3}+C