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Step-by-step Solution

Integral of $\frac{2x+3}{x^2+6x+9}$ with respect to x

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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.

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

Unlock this full step-by-step solution!

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.

Answer

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

Problem Analysis