What is the integral of 1/(5\sqrt[3]{x^5)} ?

The integral of 1/(5\sqrt[3]{x^5)} is -3/(10x^{2/3)}+C

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integral of 1/(5\sqrt[3]{x^5)}

\int \frac{1}{5 3 x ^{5}} d x

- \frac{3}{10 x ^{\frac{2}{3}}} + C

Solution steps

\int \frac{1}{5 3 x ^{5}} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{3 x ^{5}} d x

3 x^{5} = x^{\frac{5}{3}},

assuming

x \geq 0

= \frac{1}{5} \cdot \int \frac{1}{x ^{\frac{5}{3}}} d x

Apply the Power Rule

: - \frac{3}{2 x ^{\frac{2}{3}}}

= \frac{1}{5} (- \frac{3}{2 x ^{\frac{2}{3}}})

Simplify

\frac{1}{5} (- \frac{3}{2 x ^{\frac{2}{3}}}) : - \frac{3}{10 x ^{\frac{2}{3}}}

= - \frac{3}{10 x ^{\frac{2}{3}}}

Add a constant to the solution

= - \frac{3}{10 x ^{\frac{2}{3}}} + C

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What is the integral of 1/(5\sqrt[3]{x^5)} ?
The integral of 1/(5\sqrt[3]{x^5)} is -3/(10x^{2/3)}+C