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

The integral of 5x^{1/3} is 15/4 x^{4/3}+C

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integral of 5x^{1/3}

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

\frac{15}{4} x^{\frac{4}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= 5 \cdot \frac{3}{4} x^{\frac{4}{3}}

Simplify

5 \cdot \frac{3}{4} x^{\frac{4}{3}} : \frac{15}{4} x^{\frac{4}{3}}

= \frac{15}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{15}{4} x^{\frac{4}{3}} + C