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

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

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integral of (1+1/(2x))

\int (1 + \frac{1}{2 x}) d x

x + \frac{1}{2} ln ∣ x ∣ + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int \frac{1}{2 x} d x

\int 1 d x = x

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= x + \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= x + \frac{1}{2} ln ∣ x ∣ + C

\frac{x}{1 + x ^{2}}

\frac{\partial}{\partial y} (sin (x^{2} + x y))

y^{^{''}} - y = 18 t

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

f (x) = - 5 x^{2}, at x = 6

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