What is the integral of 1/(sqrt(x^7)) ?

The integral of 1/(sqrt(x^7)) is -2/(5x^{5/2)}+C

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integral of 1/(sqrt(x^7))

\int \frac{1}{x ^{7}} d x

- \frac{2}{5 x ^{\frac{5}{2}}} + C

Solution steps

\int \frac{1}{x ^{7}} d x

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

assuming

x \geq 0

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

Apply the Power Rule

= - \frac{2}{5 x ^{\frac{5}{2}}}

Add a constant to the solution

= - \frac{2}{5 x ^{\frac{5}{2}}} + C

What is the integral of 1/(sqrt(x^7)) ?
The integral of 1/(sqrt(x^7)) is -2/(5x^{5/2)}+C