What is the integral of (8x)/(3\sqrt[3]{7-2x^2)} ?

The integral of (8x)/(3\sqrt[3]{7-2x^2)} is -(7-2x^2)^{2/3}+C

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integral of (8x)/(3\sqrt[3]{7-2x^2)}

- (7 - 2 x^{2})^{\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}}

= \frac{8}{3} \cdot \frac{1}{2} (- \frac{1}{2} \cdot \frac{3}{2} v^{\frac{2}{3}})

Substitute back

= \frac{8}{3} \cdot \frac{1}{2} (- \frac{1}{2} \cdot \frac{3}{2} (7 - 2 x^{2})^{\frac{2}{3}})

Simplify

\frac{8}{3} \cdot \frac{1}{2} (- \frac{1}{2} \cdot \frac{3}{2} (7 - 2 x^{2})^{\frac{2}{3}}) : - (7 - 2 x^{2})^{\frac{2}{3}}

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

Add a constant to the solution

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

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What is the integral of (8x)/(3\sqrt[3]{7-2x^2)} ?
The integral of (8x)/(3\sqrt[3]{7-2x^2)} is -(7-2x^2)^{2/3}+C