What is the integral of 500x^{1/4} ?

The integral of 500x^{1/4} is 400x^{5/4}+C

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integral of 500x^{1/4}

\int 500 x^{\frac{1}{4}} d x

400 x^{\frac{5}{4}} + C

Solution steps

\int 500 x^{\frac{1}{4}} d x

Take the constant out:

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

= 500 \cdot \int x^{\frac{1}{4}} d x

Apply the Power Rule

= 500 \cdot \frac{4}{5} x^{\frac{5}{4}}

Simplify

500 \cdot \frac{4}{5} x^{\frac{5}{4}} : 400 x^{\frac{5}{4}}

= 400 x^{\frac{5}{4}}

Add a constant to the solution

= 400 x^{\frac{5}{4}} + C