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

The integral of (4x^2)/(\sqrt[3]{4x^3+5)} is 1/2 (4x^3+5)^{2/3}+C

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

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

= 4 \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{3}{2} v^{\frac{2}{3}}

Substitute back

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

Simplify

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

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

Add a constant to the solution

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

What is the integral of (4x^2)/(\sqrt[3]{4x^3+5)} ?
The integral of (4x^2)/(\sqrt[3]{4x^3+5)} is 1/2 (4x^3+5)^{2/3}+C