What is the integral of (20x)/(\sqrt[3]{7-3x^2)} ?

The integral of (20x)/(\sqrt[3]{7-3x^2)} is -5(-3x^2+7)^{2/3}+C

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integral of (20x)/(\sqrt[3]{7-3x^2)}

- 5 (- 3 x^{2} + 7)^{\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 the Power Rule

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

= 20 (- \frac{1}{6} \cdot \frac{3}{2} u^{\frac{2}{3}})

Substitute back

u = 7 - 3 x^{2}

= 20 (- \frac{1}{6} \cdot \frac{3}{2} (7 - 3 x^{2})^{\frac{2}{3}})

Simplify

20 (- \frac{1}{6} \cdot \frac{3}{2} (7 - 3 x^{2})^{\frac{2}{3}}) : - 5 (- 3 x^{2} + 7)^{\frac{2}{3}}

= - 5 (- 3 x^{2} + 7)^{\frac{2}{3}}

Add a constant to the solution

= - 5 (- 3 x^{2} + 7)^{\frac{2}{3}} + C

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What is the integral of (20x)/(\sqrt[3]{7-3x^2)} ?
The integral of (20x)/(\sqrt[3]{7-3x^2)} is -5(-3x^2+7)^{2/3}+C