What is the integral of (4x)/(\sqrt[3]{5+3x^2)} ?

The integral of (4x)/(\sqrt[3]{5+3x^2)} is (5+3x^2)^{2/3}+C

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integral of (4x)/(\sqrt[3]{5+3x^2)}

(5 + 3 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 the Power Rule

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

= 4 \cdot \frac{1}{6} \cdot \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = 5 + 3 x^{2}

= 4 \cdot \frac{1}{6} \cdot \frac{3}{2} (5 + 3 x^{2})^{\frac{2}{3}}

Simplify

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

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

Add a constant to the solution

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

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What is the integral of (4x)/(\sqrt[3]{5+3x^2)} ?
The integral of (4x)/(\sqrt[3]{5+3x^2)} is (5+3x^2)^{2/3}+C