What is the integral of 5/(sqrt(x^8)) ?

The integral of 5/(sqrt(x^8)) is -5/(3x^3)+C

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integral of 5/(sqrt(x^8))

\int \frac{5}{x ^{8}} d x

- \frac{5}{3 x ^{3}} + C

Solution steps

\int \frac{5}{x ^{8}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x ^{8}} d x

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

assuming

x \geq 0

= 5 \cdot \int \frac{1}{x ^{4}} d x

Apply the Power Rule

= 5 (- \frac{1}{3 x ^{3}})

Simplify

5 (- \frac{1}{3 x ^{3}}) : - \frac{5}{3 x ^{3}}

= - \frac{5}{3 x ^{3}}

Add a constant to the solution

= - \frac{5}{3 x ^{3}} + C

What is the integral of 5/(sqrt(x^8)) ?
The integral of 5/(sqrt(x^8)) is -5/(3x^3)+C