# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_0^2\left(\left(\frac{2x-1}{\left(x+3\right)^2}\right)\right)dx$

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

$\begin{matrix}u=x+3 \\ du=dx\end{matrix}$

Learn how to solve definite integrals problems step by step online. Integrate (2x-1)/((x+3)^2) from 0 to 2. Solve the integral \int_{0}^{2}\frac{2x-1}{\left(x+3\right)^2}dx applying u-substitution. Let u and du be. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify. Multiplying polynomials 2 and u-3.

$\frac{31}{351}$$\,\,\left(\approx 0.08831791419864787\right)$

### Problem Analysis

$\int_0^2\left(\left(\frac{2x-1}{\left(x+3\right)^2}\right)\right)dx$

### Main topic:

Definite integrals

~ 2.78 seconds