What is the integral of 3/(5x^{2/5)} ?

The integral of 3/(5x^{2/5)} is x^{3/5}+C

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integral of 3/(5x^{2/5)}

\int \frac{3}{5 x ^{\frac{2}{5}}} d x

x^{\frac{3}{5}} + C

Solution steps

\int \frac{3}{5 x ^{\frac{2}{5}}} d x

Take the constant out:

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

= \frac{3}{5} \cdot \int \frac{1}{x ^{\frac{2}{5}}} d x

Apply the Power Rule

: \frac{5}{3} x^{\frac{3}{5}}

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

Simplify

\frac{3}{5} \cdot \frac{5}{3} x^{\frac{3}{5}} : x^{\frac{3}{5}}

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

Add a constant to the solution

= x^{\frac{3}{5}} + C

x \to 2 lim (\frac{2 x ^{2} - 5 x + 2}{x ^{3} - 2 x ^{2}})

\frac{d}{d x} (a x^{2} e^{- 3 x})

\frac{\partial}{\partial x} (x^{4} - 8 x y - 5 y^{2})

\frac{\partial}{\partial x} (ln (x^{2} + y^{2} + z^{2}))

What is the integral of 3/(5x^{2/5)} ?
The integral of 3/(5x^{2/5)} is x^{3/5}+C