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

The integral of (2x^4)/(\sqrt[3]{x^2)} is 6/13 x^{13/3}+C

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

\frac{6}{13} x^{\frac{13}{3}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= 2 \cdot \int \frac{x ^{4}}{x ^{\frac{2}{3}}} d x

Simplify

\frac{x ^{4}}{x ^{\frac{2}{3}}} : x^{\frac{10}{3}}

= 2 \cdot \int x^{\frac{10}{3}} d x

Apply the Power Rule

: \frac{3}{13} x^{\frac{13}{3}}

= 2 \cdot \frac{3}{13} x^{\frac{13}{3}}

Simplify

2 \cdot \frac{3}{13} x^{\frac{13}{3}} : \frac{6}{13} x^{\frac{13}{3}}

= \frac{6}{13} x^{\frac{13}{3}}

Add a constant to the solution

= \frac{6}{13} x^{\frac{13}{3}} + C

\int (\frac{e ^{x}}{2} + x x) d x

y^{^{'}} = \frac{4 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2}}{x ^{6} y}

\frac{d}{d x} (\frac{sin ( x )}{ln ( x )})

\frac{d}{d x} (arctan (2 x^{2} - 4))

y^{^{''}} - 8 y^{^{'}} + 16 = 0

What is the integral of (2x^4)/(\sqrt[3]{x^2)} ?
The integral of (2x^4)/(\sqrt[3]{x^2)} is 6/13 x^{13/3}+C