What is the integral of 1/(sqrt(x^8)) ?

The integral of 1/(sqrt(x^8)) is -1/(3x^3)+C

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integral of 1/(sqrt(x^8))

\int \frac{1}{x ^{8}} d x

- \frac{1}{3 x ^{3}} + C

Solution steps

\int \frac{1}{x ^{8}} d x

x^{8} = x^{4},

assuming

x \geq 0

= \int \frac{1}{x ^{4}} d x

Apply the Power Rule

: - \frac{1}{3 x ^{3}}

= - \frac{1}{3 x ^{3}}

Add a constant to the solution

= - \frac{1}{3 x ^{3}} + C

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What is the integral of 1/(sqrt(x^8)) ?
The integral of 1/(sqrt(x^8)) is -1/(3x^3)+C