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))

integral

\frac{1}{( 2 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

\frac{ln ( x )}{( 1 + 2 x ) ^{2}}

\frac{1}{( 100 - n )}

\frac{- 1}{x ^{3}}

a + 3 c - 2 d

(1 - 0.1 x)^{- 2}