What is the integral of \sqrt[3]{27x^5} ?

The integral of \sqrt[3]{27x^5} is 9/8 x^{8/3}+C

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integral of \sqrt[3]{27x^5}

\frac{9}{8} x^{\frac{8}{3}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= 3 \cdot \int x^{\frac{5}{3}} d x

Apply the Power Rule

: \frac{3}{8} x^{\frac{8}{3}}

= 3 \cdot \frac{3}{8} x^{\frac{8}{3}}

Simplify

3 \cdot \frac{3}{8} x^{\frac{8}{3}} : \frac{9}{8} x^{\frac{8}{3}}

= \frac{9}{8} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{9}{8} x^{\frac{8}{3}} + C

f (x) = \frac{1}{x - 1}, (- 7, - \frac{1}{8})

\frac{d}{d x} (3 x^{5} (7 - 2 x)^{7})

(x^{2} - 4), y = 0, x = - 4, x = 3

\int \frac{e ^{5 s i n (x)}}{sec ( x )} d x

\frac{d}{d x} (\frac{( 3 x - 5 ) ^{3}}{( 2 x ^{2} + 1 ) ^{4}})

What is the integral of \sqrt[3]{27x^5} ?
The integral of \sqrt[3]{27x^5} is 9/8 x^{8/3}+C