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

The integral of (x^2)/(\sqrt[4]{x^3+2)} is 4/9 (x^3+2)^{3/4}+C

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

\frac{4}{9} (x^{3} + 2)^{\frac{3}{4}} + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply u-substitution

Apply the Power Rule

: \frac{4}{3} v^{\frac{3}{4}}

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

Substitute back

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

Simplify

\frac{1}{3} \cdot \frac{4}{3} (x^{3} + 2)^{\frac{3}{4}} : \frac{4}{9} (x^{3} + 2)^{\frac{3}{4}}

= \frac{4}{9} (x^{3} + 2)^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{9} (x^{3} + 2)^{\frac{3}{4}} + C

x \frac{d y}{d x} = y^{2} + y

\int_{0}^{4} x - 1 d x

y = 5 - x^{2}

\int (6 x + 5) 3 x^{2} + 5 x d x

t \to 0 lim (\frac{4 t ^{2} + 3 t + 2}{t ^{3} + 2 t - 6})

What is the integral of (x^2)/(\sqrt[4]{x^3+2)} ?
The integral of (x^2)/(\sqrt[4]{x^3+2)} is 4/9 (x^3+2)^{3/4}+C