Final answer to the problem
$\frac{2}{3}\ln\left|x\right|-\frac{2}{3}\ln\left|x+3\right|+C_0$
Got another answer? Verify it here!
Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(2/(x(x+3)))dx. Rewrite the fraction \frac{2}{x\left(x+3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{3x}+\frac{-2}{3\left(x+3\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{3x}dx results in: \frac{2}{3}\ln\left(x\right). The integral \int\frac{-2}{3\left(x+3\right)}dx results in: -\frac{2}{3}\ln\left(x+3\right).
Final answer to the problem
$\frac{2}{3}\ln\left|x\right|-\frac{2}{3}\ln\left|x+3\right|+C_0$
