What is the integral of 2/(5x^{9/4)} ?

The integral of 2/(5x^{9/4)} is -8/(25x^{5/4)}+C

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integral of 2/(5x^{9/4)}

\int \frac{2}{5 x ^{\frac{9}{4}}} d x

- \frac{8}{25 x ^{\frac{5}{4}}} + C

Solution steps

\int \frac{2}{5 x ^{\frac{9}{4}}} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int \frac{1}{x ^{\frac{9}{4}}} d x

Apply the Power Rule

: - \frac{4}{5 x ^{\frac{5}{4}}}

= \frac{2}{5} (- \frac{4}{5 x ^{\frac{5}{4}}})

Simplify

\frac{2}{5} (- \frac{4}{5 x ^{\frac{5}{4}}}) : - \frac{8}{25 x ^{\frac{5}{4}}}

= - \frac{8}{25 x ^{\frac{5}{4}}}

Add a constant to the solution

= - \frac{8}{25 x ^{\frac{5}{4}}} + C

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What is the integral of 2/(5x^{9/4)} ?
The integral of 2/(5x^{9/4)} is -8/(25x^{5/4)}+C