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

The integral of (5x)/(3x^{1/3)} is x^{5/3}+C

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integral of (5x)/(3x^{1/3)}

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

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

y = 1.1 x + e^{x}, (0, 1)

y = 0, y = x^{2}, y = 4 x - x^{2}, [0, 2]

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t), y (0) = 0

(x^{2} + 5) (8 - x)

What is the integral of (5x)/(3x^{1/3)} ?
The integral of (5x)/(3x^{1/3)} is x^{5/3}+C