What is the integral of 20\sqrt[3]{3x-2} ?

The integral of 20\sqrt[3]{3x-2} is 5(3x-2)^{4/3}+C

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integral of 20\sqrt[3]{3x-2}

5 (3 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

= 20 \cdot \frac{1}{3} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = 3 x - 2

= 20 \cdot \frac{1}{3} \cdot \frac{3}{4} (3 x - 2)^{\frac{4}{3}}

Simplify

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

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

Add a constant to the solution

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

What is the integral of 20\sqrt[3]{3x-2} ?
The integral of 20\sqrt[3]{3x-2} is 5(3x-2)^{4/3}+C