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

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

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

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

6 x + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{1}{4 x ^{2}} d x

4 x^{2} = x,

assuming

x \geq 0

= 3 \cdot \int \frac{1}{x} d x

Apply the Power Rule

: 2 x^{\frac{1}{2}}

= 3 \cdot 2 x^{\frac{1}{2}}

Simplify

3 \cdot 2 x^{\frac{1}{2}} : 6 x

= 6 x

Add a constant to the solution

= 6 x + C

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