What is the integral of 7/(2\sqrt[4]{x^9)} ?

The integral of 7/(2\sqrt[4]{x^9)} is -(14)/(5x^{5/4)}+C

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integral of 7/(2\sqrt[4]{x^9)}

- \frac{14}{5 x ^{\frac{5}{4}}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= \frac{7}{2} \cdot \int \frac{1}{x ^{\frac{9}{4}}} d x

Apply the Power Rule

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

= \frac{7}{2} (- \frac{4}{5 x ^{\frac{5}{4}}})

Simplify

\frac{7}{2} (- \frac{4}{5 x ^{\frac{5}{4}}}) : - \frac{14}{5 x ^{\frac{5}{4}}}

= - \frac{14}{5 x ^{\frac{5}{4}}}

Add a constant to the solution

= - \frac{14}{5 x ^{\frac{5}{4}}} + C

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What is the integral of 7/(2\sqrt[4]{x^9)} ?
The integral of 7/(2\sqrt[4]{x^9)} is -(14)/(5x^{5/4)}+C