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

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

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

- 5 (- x^{3} + 3)^{\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

Take the constant out:

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

Apply the Power Rule

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

= 10 \cdot \frac{1}{3} (- \frac{3}{2} v^{\frac{2}{3}})

Substitute back

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

Simplify

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

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

Add a constant to the solution

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

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