What is the integral of-1/(2x) ?

The integral of-1/(2x) is -1/2 ln|x|+C

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integral of-1/(2x)

\int - \frac{1}{2 x} d x

- \frac{1}{2} ln ∣ x ∣ + C

Solution steps

\int - \frac{1}{2 x} d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ x ∣ + C

x \to \frac{π}{3} - lim (cot (3 x))

f (x) = x^{2} - 4, (3, 5)

\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})

sin^{2} (π t)

n = 1 \sum \infty n