What is the integral of-10x^{2/3} ?

The integral of-10x^{2/3} is -6x^{5/3}+C

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integral of-10x^{2/3}

\int - 10 x^{\frac{2}{3}} d x

- 6 x^{\frac{5}{3}} + C

Solution steps

\int - 10 x^{\frac{2}{3}} d x

Take the constant out:

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

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

Apply the Power Rule

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

= - 10 \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

- 10 \cdot \frac{3}{5} x^{\frac{5}{3}} : - 6 x^{\frac{5}{3}}

= - 6 x^{\frac{5}{3}}

Add a constant to the solution

= - 6 x^{\frac{5}{3}} + C

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cos (x^{2} + 5) - x^{3}

\frac{d}{d x} (ln (\frac{5 + e ^{x}}{5 - e ^{x}}))