What is the integral of 10\sqrt[3]{t^2} ?

The integral of 10\sqrt[3]{t^2} is 6t^{5/3}+C

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integral of 10\sqrt[3]{t^2}

6 t^{\frac{5}{3}} + C

Solution steps

Take the constant out:

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

assuming

t \geq 0

= 10 \cdot \int t^{\frac{2}{3}} d t

Apply the Power Rule

= 10 \cdot \frac{3}{5} t^{\frac{5}{3}}

Simplify

10 \cdot \frac{3}{5} t^{\frac{5}{3}} : 6 t^{\frac{5}{3}}

= 6 t^{\frac{5}{3}}

Add a constant to the solution

= 6 t^{\frac{5}{3}} + C

What is the integral of 10\sqrt[3]{t^2} ?
The integral of 10\sqrt[3]{t^2} is 6t^{5/3}+C