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

The integral of 1/(8x) is 1/8 ln|x|+C

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integral of 1/(8x)

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

\frac{1}{8} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{8} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{8} ln ∣ x ∣ + C

n = 0 \sum \infty \frac{1}{n} x^{n}

\int sec^{3} (z) d z

\frac{d}{d x} (sin (\frac{π x}{3}))

f (x) = ln (x^{2} + x + 1)

y^{^{''''}} - y = 0