What is the integral of (4x)/(\sqrt[3]{2000+x^2)} ?

The integral of (4x)/(\sqrt[3]{2000+x^2)} is 3(x^2+2000)^{2/3}+C

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integral of (4x)/(\sqrt[3]{2000+x^2)}

3 (x^{2} + 2000)^{\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}{2} \cdot \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = 2000 + x^{2}

= 4 \cdot \frac{1}{2} \cdot \frac{3}{2} (2000 + x^{2})^{\frac{2}{3}}

Simplify

4 \cdot \frac{1}{2} \cdot \frac{3}{2} (2000 + x^{2})^{\frac{2}{3}} : 3 (x^{2} + 2000)^{\frac{2}{3}}

= 3 (x^{2} + 2000)^{\frac{2}{3}}

Add a constant to the solution

= 3 (x^{2} + 2000)^{\frac{2}{3}} + C

y = (x^{2} + 7 x + 1)^{3}

\frac{\partial}{\partial x} (e^{2 z} - x yz)

\int x 1 - x d x

9 y^{^{''}} - 81 y = 0

2 t^{3 π}

What is the integral of (4x)/(\sqrt[3]{2000+x^2)} ?
The integral of (4x)/(\sqrt[3]{2000+x^2)} is 3(x^2+2000)^{2/3}+C