What is the integral of x*\sqrt[3]{x^{10}} ?

The integral of x*\sqrt[3]{x^{10}} is 3/16 x^{16/3}+C

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integral of x*\sqrt[3]{x^{10}}

\frac{3}{16} x^{\frac{16}{3}} + C

Solution steps

assuming

x \geq 0

= \int x x^{\frac{10}{3}} d x

Simplify

x x^{\frac{10}{3}} : x^{\frac{13}{3}}

= \int x^{\frac{13}{3}} d x

Apply the Power Rule

= \frac{3}{16} x^{\frac{16}{3}}

Add a constant to the solution

= \frac{3}{16} x^{\frac{16}{3}} + C

What is the integral of x*\sqrt[3]{x^{10}} ?
The integral of x*\sqrt[3]{x^{10}} is 3/16 x^{16/3}+C