What is the integral of 4x^{5/4} ?

The integral of 4x^{5/4} is 16/9 x^{9/4}+C

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integral of 4x^{5/4}

\int 4 x^{\frac{5}{4}} d x

\frac{16}{9} x^{\frac{9}{4}} + C

Solution steps

\int 4 x^{\frac{5}{4}} d x

Take the constant out:

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

= 4 \cdot \int x^{\frac{5}{4}} d x

Apply the Power Rule

: \frac{4}{9} x^{\frac{9}{4}}

= 4 \cdot \frac{4}{9} x^{\frac{9}{4}}

Simplify

4 \cdot \frac{4}{9} x^{\frac{9}{4}} : \frac{16}{9} x^{\frac{9}{4}}

= \frac{16}{9} x^{\frac{9}{4}}

Add a constant to the solution

= \frac{16}{9} x^{\frac{9}{4}} + C

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