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

The integral of 2/(\sqrt[4]{x^5)} is -8/(\sqrt[4]{x)}+C

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

\int \frac{2}{4 x ^{5}} d x

- \frac{8}{4 x} + C

Solution steps

\int \frac{2}{4 x ^{5}} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{4 x ^{5}} d x

Apply exponent rule:

(a^{n})^{m} = a^{n \cdot m}

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

= 2 \cdot \int \frac{1}{x ^{\frac{5}{4}}} d x

Apply the Power Rule

: - \frac{4}{4 x}

= 2 (- \frac{4}{4 x})

Simplify

2 (- \frac{4}{4 x}) : - \frac{8}{4 x}

= - \frac{8}{4 x}

Add a constant to the solution

= - \frac{8}{4 x} + C

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What is the integral of 2/(\sqrt[4]{x^5)} ?
The integral of 2/(\sqrt[4]{x^5)} is -8/(\sqrt[4]{x)}+C