What is the integral of 7\sqrt[3]{x^2} ?

The integral of 7\sqrt[3]{x^2} is 21/5 x^{5/3}+C

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integral of 7\sqrt[3]{x^2}

\int 7 3 x^{2} d x

\frac{21}{5} x^{\frac{5}{3}} + C

Solution steps

\int 7 3 x^{2} d x

Take the constant out:

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

= 7 \cdot \int 3 x^{2} d x

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

assuming

x \geq 0

= 7 \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

: \frac{3}{5} x^{\frac{5}{3}}

= 7 \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

7 \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{21}{5} x^{\frac{5}{3}}

= \frac{21}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{21}{5} x^{\frac{5}{3}} + C

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What is the integral of 7\sqrt[3]{x^2} ?
The integral of 7\sqrt[3]{x^2} is 21/5 x^{5/3}+C