What is the integral of 2x^{1/4} ?

The integral of 2x^{1/4} is 8/5 x^{5/4}+C

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integral of 2x^{1/4}

\int 2 x^{\frac{1}{4}} d x

\frac{8}{5} x^{\frac{5}{4}} + C

Solution steps

\int 2 x^{\frac{1}{4}} d x

Take the constant out:

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

= 2 \cdot \int x^{\frac{1}{4}} d x

Apply the Power Rule

= 2 \cdot \frac{4}{5} x^{\frac{5}{4}}

Simplify

2 \cdot \frac{4}{5} x^{\frac{5}{4}} : \frac{8}{5} x^{\frac{5}{4}}

= \frac{8}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{8}{5} x^{\frac{5}{4}} + C

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