What is the integral of \sqrt[3]{4x^2-2x}(4x-1) ?

The integral of \sqrt[3]{4x^2-2x}(4x-1) is 3/8 (4x^2-2x)^{4/3}+C

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integral of \sqrt[3]{4x^2-2x}(4x-1)

\frac{3}{8} (4 x^{2} - 2 x)^{\frac{4}{3}} + C

Solution steps

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{1}{2} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = 4 x^{2} - 2 x

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

Simplify

\frac{1}{2} \cdot \frac{3}{4} (4 x^{2} - 2 x)^{\frac{4}{3}} : \frac{3}{8} (4 x^{2} - 2 x)^{\frac{4}{3}}

= \frac{3}{8} (4 x^{2} - 2 x)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{8} (4 x^{2} - 2 x)^{\frac{4}{3}} + C

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What is the integral of \sqrt[3]{4x^2-2x}(4x-1) ?
The integral of \sqrt[3]{4x^2-2x}(4x-1) is 3/8 (4x^2-2x)^{4/3}+C