What is the integral of (-5x^2)/(\sqrt[3]{14-x^3)} ?

The integral of (-5x^2)/(\sqrt[3]{14-x^3)} is 5/2 (14-x^3)^{2/3}+C

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integral of (-5x^2)/(\sqrt[3]{14-x^3)}

\frac{5}{2} (14 - x^{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}}

= - 5 \cdot \frac{1}{3} (- \frac{3}{2} v^{\frac{2}{3}})

Substitute back

= - 5 \cdot \frac{1}{3} (- \frac{3}{2} (14 - x^{3})^{\frac{2}{3}})

Simplify

- 5 \cdot \frac{1}{3} (- \frac{3}{2} (14 - x^{3})^{\frac{2}{3}}) : \frac{5}{2} (14 - x^{3})^{\frac{2}{3}}

= \frac{5}{2} (14 - x^{3})^{\frac{2}{3}}

Add a constant to the solution

= \frac{5}{2} (14 - x^{3})^{\frac{2}{3}} + C

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What is the integral of (-5x^2)/(\sqrt[3]{14-x^3)} ?
The integral of (-5x^2)/(\sqrt[3]{14-x^3)} is 5/2 (14-x^3)^{2/3}+C