What is the integral of 1/(5\sqrt[5]{x^4)} ?

The integral of 1/(5\sqrt[5]{x^4)} is \sqrt[5]{x}+C

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integral of 1/(5\sqrt[5]{x^4)}

Solution steps

Take the constant out:

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

assuming

x \geq 0

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

Apply the Power Rule

: 5 x^{\frac{1}{5}}

= \frac{1}{5} \cdot 5 x^{\frac{1}{5}}

Simplify

Add a constant to the solution

\int (\frac{2}{x + x ^{3} - 5 x}) d x

\int \frac{1}{sec ( x ) - tan ( x )} d x

\int sin (2 x) e^{- 2 x} d x

\int (sin (nπ x)) d x

\int (2 \frac{sin ( 2 x )}{sin ( x )}) d x

What is the integral of 1/(5\sqrt[5]{x^4)} ?
The integral of 1/(5\sqrt[5]{x^4)} is \sqrt[5]{x}+C