What is the integral of (4x^2)/(\sqrt[3]{x^3-6)} ?

The integral of (4x^2)/(\sqrt[3]{x^3-6)} is 2(x^3-6)^{2/3}+C

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integral of (4x^2)/(\sqrt[3]{x^3-6)}

2 (x^{3} - 6)^{\frac{2}{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 u-substitution

Apply the Power Rule

: \frac{3}{2} v^{\frac{2}{3}}

= 4 \cdot \frac{1}{3} \cdot \frac{3}{2} v^{\frac{2}{3}}

Substitute back

= 4 \cdot \frac{1}{3} \cdot \frac{3}{2} (x^{3} - 6)^{\frac{2}{3}}

Simplify

4 \cdot \frac{1}{3} \cdot \frac{3}{2} (x^{3} - 6)^{\frac{2}{3}} : 2 (x^{3} - 6)^{\frac{2}{3}}

= 2 (x^{3} - 6)^{\frac{2}{3}}

Add a constant to the solution

= 2 (x^{3} - 6)^{\frac{2}{3}} + C

- x^{2} - 2 x + 9, [- 4, 0]

f (x) = arcsin (8 t)

\frac{d}{d x} (\frac{1}{4} e^{x} + e^{- x})

\frac{d}{d x} (\frac{d y}{d x}) + 4 y = 0

\int \frac{sin ^{2} ( x )}{x} d x

What is the integral of (4x^2)/(\sqrt[3]{x^3-6)} ?
The integral of (4x^2)/(\sqrt[3]{x^3-6)} is 2(x^3-6)^{2/3}+C