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

The integral of (6x)/(\sqrt[4]{x^3)} is 24/5 x^{5/4}+C

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integral of (6x)/(\sqrt[4]{x^3)}

\int \frac{6 x}{4 x ^{3}} d x

\frac{24}{5} x^{\frac{5}{4}} + C

Solution steps

\int \frac{6 x}{4 x ^{3}} d x

Take the constant out:

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

= 6 \cdot \int \frac{x}{4 x ^{3}} d x

4 x^{3} = x^{\frac{3}{4}},

assuming

x \geq 0

= 6 \cdot \int \frac{x}{x ^{\frac{3}{4}}} d x

Simplify

\frac{x}{x ^{\frac{3}{4}}} : x^{\frac{1}{4}}

= 6 \cdot \int x^{\frac{1}{4}} d x

Apply the Power Rule

: \frac{4}{5} x^{\frac{5}{4}}

= 6 \cdot \frac{4}{5} x^{\frac{5}{4}}

Simplify

6 \cdot \frac{4}{5} x^{\frac{5}{4}} : \frac{24}{5} x^{\frac{5}{4}}

= \frac{24}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{24}{5} x^{\frac{5}{4}} + C

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What is the integral of (6x)/(\sqrt[4]{x^3)} ?
The integral of (6x)/(\sqrt[4]{x^3)} is 24/5 x^{5/4}+C