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

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

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integral of 1/(2(x))

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

(4 x^{2} + 5)^{4}

(x + 1) sin (x^{2} + 2 x + 3)

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

ln (a^{2} - x^{2})

(x^{3} - 1)^{5}