Final answer to the problem
$\frac{1}{3}\ln\left|3x+2\right|+\frac{7}{3\left(3x+2\right)}+C_0$
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Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((3x-5)/(9x^2+12x+4))dx. Rewrite the expression \frac{3x-5}{9x^2+12x+4} inside the integral in factored form. Rewrite the fraction \frac{3x-5}{\left(3x+2\right)^{2}} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{3x+2}+\frac{-7}{\left(3x+2\right)^{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{3x+2}dx results in: \frac{1}{3}\ln\left(3x+2\right).
Final answer to the problem
$\frac{1}{3}\ln\left|3x+2\right|+\frac{7}{3\left(3x+2\right)}+C_0$
