Exercise
$\int\frac{3x}{\left(x^2-9\right)}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((3x)/(x^2-9))dx. Rewrite the expression \frac{3x}{x^2-9} inside the integral in factored form. Take out the constant 3 from the integral. Rewrite the fraction \frac{x}{\left(x+3\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2\left(x+3\right)}+\frac{1}{2\left(x-3\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral int((3x)/(x^2-9))dx
Final answer to the exercise
$\frac{3}{2}\ln\left|x+3\right|+\frac{3}{2}\ln\left|x-3\right|+C_0$