What is the integral of-30t^{2/3} ?

The integral of-30t^{2/3} is -18t^{5/3}+C

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integral of-30t^{2/3}

\int - 30 t^{\frac{2}{3}} d t

- 18 t^{\frac{5}{3}} + C

Solution steps

\int - 30 t^{\frac{2}{3}} d t

Take the constant out:

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

= - 30 \cdot \int t^{\frac{2}{3}} d t

Apply the Power Rule

= - 30 \cdot \frac{3}{5} t^{\frac{5}{3}}

Simplify

- 30 \cdot \frac{3}{5} t^{\frac{5}{3}} : - 18 t^{\frac{5}{3}}

= - 18 t^{\frac{5}{3}}

Add a constant to the solution

= - 18 t^{\frac{5}{3}} + C