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

The integral of (8x)/(sqrt(x^5)) is -(16)/(sqrt(x))+C

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

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

- \frac{16}{x} + C

Solution steps

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

Take the constant out:

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

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

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

assuming

x \geq 0

= 8 \cdot \int \frac{x}{x ^{\frac{5}{2}}} d x

Simplify

\frac{x}{x ^{\frac{5}{2}}} : \frac{1}{x ^{\frac{3}{2}}}

= 8 \cdot \int \frac{1}{x ^{\frac{3}{2}}} d x

Apply the Power Rule

= 8 (- \frac{2}{x})

Simplify

8 (- \frac{2}{x}) : - \frac{16}{x}

= - \frac{16}{x}

Add a constant to the solution

= - \frac{16}{x} + C

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What is the integral of (8x)/(sqrt(x^5)) ?
The integral of (8x)/(sqrt(x^5)) is -(16)/(sqrt(x))+C