Evaluate using formulas and rules of \int (2x)/(2x-1)

x+\frac{1}{2}\ln{\left(\left|2x-1\right|\right)}+C,C \in \mathbb{R}

Solve int (2x)/(2x-1)

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Use the property of integral \int k f (x) d x = k \int f (x) d x

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

Rewrite the fraction

2 \times \int (\frac{1}{2} + \frac{1}{4 x - 2}) d x

Use the property of integral \int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

2 (\int \frac{1}{2} d x + \int \frac{1}{4 x - 2} d x)

Calculate

2 \times \int \frac{1}{2} d x + 2 \times \int \frac{1}{4 x - 2} d x

Evaluate the integral

More Steps

x + 2 \times \int \frac{1}{4 x - 2} d x

Evaluate the integral

More Steps

x + \frac{1}{2} ln (∣ 2 x - 1 ∣)

Solution

x + \frac{1}{2} ln (∣ 2 x - 1 ∣) + C, C \in R