# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_1^{\infty}\left(\frac{x-2}{x\cdot\left(x^2+1\right)}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\frac{x-2}{x\left(x^2+1\right)}=\frac{A}{x}+\frac{Bx+C}{x^2+1}$

Learn how to solve definite integrals problems step by step online. Integrate (x-2)/(x(x^2+1)) from 1 to \infty. Rewrite the fraction \frac{x-2}{x\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by x\left(x^2+1\right). Multiplying polynomials. Simplifying.

$0.0923-2\ln\left|\infty \right|+\ln\left|\infty \right|$

### Problem Analysis

$\int_1^{\infty}\left(\frac{x-2}{x\cdot\left(x^2+1\right)}\right)dx$

### Main topic:

Definite integrals

~ 0.35 seconds