# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{x+2}{2x^2-x}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\left(\frac{x}{2x^2-x}+\frac{2}{2x^2-x}\right)dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (x+2)/(2x^2-x) with respect to x. Split the fraction \frac{x+2}{2x^2-x} inside the integral, in two terms with common denominator 2x^2-x. The integral of the sum of two or more functions is equal to the sum of their integrals. The integral \int\frac{x}{2x^2-x}dx results in: \frac{1}{2}\ln\left|2x-1\right|. The integral \int\frac{2}{2x^2-x}dx results in: -2\ln\left|x\right|.

$\frac{5}{2}\ln\left|2x-1\right|-2\ln\left|x\right|+C_0$

### Problem Analysis

$\int\frac{x+2}{2x^2-x}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.18 seconds