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The trinomial $x^2+6x+9$ is a perfect square trinomial, because it's discriminant is equal to zero
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$\Delta=b^2-4ac=6^2-4\left(1\right)\left(9\right) = 0$
Learn how to solve differential equations problems step by step online. Find the integral int((2x+3)/(x^2+6x+9))dx. The trinomial x^2+6x+9 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can solve the integral \int\frac{2x+3}{\left(x+3\right)^{2}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.