What is the integral of (-4)/(sqrt(x^9)) ?

The integral of (-4)/(sqrt(x^9)) is 8/(7x^{7/2)}+C

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integral of (-4)/(sqrt(x^9))

\int \frac{- 4}{x ^{9}} d x

\frac{8}{7 x ^{\frac{7}{2}}} + C

Solution steps

\int \frac{- 4}{x ^{9}} d x

Take the constant out:

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

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

x^{9} = x^{\frac{9}{2}},

assuming

x \geq 0

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

Apply the Power Rule

: - \frac{2}{7 x ^{\frac{7}{2}}}

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

Simplify

- 4 (- \frac{2}{7 x ^{\frac{7}{2}}}) : \frac{8}{7 x ^{\frac{7}{2}}}

= \frac{8}{7 x ^{\frac{7}{2}}}

Add a constant to the solution

= \frac{8}{7 x ^{\frac{7}{2}}} + C

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What is the integral of (-4)/(sqrt(x^9)) ?
The integral of (-4)/(sqrt(x^9)) is 8/(7x^{7/2)}+C