What is the integral of \sqrt[3]{64x^5} ?

The integral of \sqrt[3]{64x^5} is 3/2 x^{8/3}+C

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integral of \sqrt[3]{64x^5}

\int 3 64 x^{5} d x

\frac{3}{2} x^{\frac{8}{3}} + C

Solution steps

\int 3 64 x^{5} d x

3 64 x^{5} = 364 3 x^{5}

= \int 364 3 x^{5} d x

Take the constant out:

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

= 364 \cdot \int 3 x^{5} d x

364 = 4

= 4 \cdot \int 3 x^{5} d x

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

assuming

x \geq 0

= 4 \cdot \int x^{\frac{5}{3}} d x

Apply the Power Rule

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

= 4 \cdot \frac{3}{8} x^{\frac{8}{3}}

Simplify

4 \cdot \frac{3}{8} x^{\frac{8}{3}} : \frac{3}{2} x^{\frac{8}{3}}

= \frac{3}{2} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{3}{2} x^{\frac{8}{3}} + C

\int_{- 18}^{32} \frac{1}{∣ 2 x ∣} d x

3 - \frac{2}{s - 1}

x^{2} - 6 x + 9, x^{2} - x + 6, [0, 5]

t \frac{d y}{d t} = t^{3} + 6 t^{3} y

x \to 0 + lim (x (12))

What is the integral of \sqrt[3]{64x^5} ?
The integral of \sqrt[3]{64x^5} is 3/2 x^{8/3}+C