What is the integral of (10\sqrt[3]{5x-2})/3 ?

The integral of (10\sqrt[3]{5x-2})/3 is 1/2 (5x-2)^{4/3}+C

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integral of (10\sqrt[3]{5x-2})/3

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

Solution steps

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= \frac{10}{3} \cdot \frac{1}{5} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = 5 x - 2

= \frac{10}{3} \cdot \frac{1}{5} \cdot \frac{3}{4} (5 x - 2)^{\frac{4}{3}}

Simplify

\frac{10}{3} \cdot \frac{1}{5} \cdot \frac{3}{4} (5 x - 2)^{\frac{4}{3}} : \frac{1}{2} (5 x - 2)^{\frac{4}{3}}

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

Add a constant to the solution

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

\int_{0}^{3} 1 + 16 x^{2} d x

x^{2}

(4 x y^{2} + 3 y) d x + (4 x^{2} y + 3 x) d y = 0

\frac{2250}{5 x ^{2} + x}

(- 12) (- 1 - 3)

What is the integral of (10\sqrt[3]{5x-2})/3 ?
The integral of (10\sqrt[3]{5x-2})/3 is 1/2 (5x-2)^{4/3}+C