What is the integral of 9x^{2/3} ?

The integral of 9x^{2/3} is 27/5 x^{5/3}+C

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integral of 9x^{2/3}

\int 9 x^{\frac{2}{3}} d x

\frac{27}{5} x^{\frac{5}{3}} + C

Solution steps

\int 9 x^{\frac{2}{3}} d x

Take the constant out:

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

= 9 \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

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

= 9 \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

9 \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{27}{5} x^{\frac{5}{3}}

= \frac{27}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{27}{5} x^{\frac{5}{3}} + C

x \to - \infty lim (3 - 2^{x})

ln (\frac{x}{x ^{2} + c})

\int_{0}^{8} \frac{2}{x ^{\frac{2}{3}}} d x

\frac{d}{d x} (\frac{5}{x} - 1)

f (x) = x^{4} - 13 x^{2} + 36, at 1