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

-\frac{1}{2}x-\frac{1}{4}\ln{\left(\left|2x-1\right|\right)}+C,C \in \mathbb{R}

Solve int x/(1-2x)

Evaluate

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

Remove the parentheses

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

Rearrange the terms

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

Rewrite the fraction

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

Calculate

\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

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

Use the property of integral \int k d x = k x

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

Evaluate the integral

More Steps

- \frac{1}{2} x - \frac{1}{4} ln (∣ 2 x - 1 ∣)

Solution

- \frac{1}{2} x - \frac{1}{4} ln (∣ 2 x - 1 ∣) + C, C \in R