# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\:\frac{2x+3}{\:x^2+6x+9}dx$

Learn how to solve integrals of rational functions problems step by step online.

$\Delta=b^2-4ac=6^2-4\left(1\right)\left(9\right) = 0$

Learn how to solve integrals of rational functions problems step by step online. Integral of (2x+3)/(x^2+6x+9) with respect to x. The trinomial x^2+6x+9 is perfect square, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. Solve the integral \int\frac{2x+3}{\left(x+3\right)^{2}}dx applying u-substitution. Let u and du be.

$\frac{3}{x+3}+2\ln\left|x+3\right|+C_0$

### Problem Analysis

$\int\:\frac{2x+3}{\:x^2+6x+9}dx$

### Main topic:

Integrals of Rational Functions

~ 0.18 seconds