What is the integral of (8/x) ?

The integral of (8/x) is 8ln|x|+C

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integral of (8/x)

\int (\frac{8}{x}) d x

8 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 8 ln ∣ x ∣

Add a constant to the solution

= 8 ln ∣ x ∣ + C

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\frac{\partial}{\partial x} (cos (x y) y)