What is the integral of 1/(sqrt(x^9)) ?

The integral of 1/(sqrt(x^9)) is -2/(7x^{7/2)}+C

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integral of 1/(sqrt(x^9))

\int \frac{1}{x ^{9}} d x

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

Solution steps

\int \frac{1}{x ^{9}} d x

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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What is the integral of 1/(sqrt(x^9)) ?
The integral of 1/(sqrt(x^9)) is -2/(7x^{7/2)}+C