Learn how to solve problems step by step online. Find the integral int((x-3)/((x^2+9)(x^2-4)))dx. Rewrite the expression \frac{x-3}{\left(x^2+9\right)\left(x^2-4\right)} inside the integral in factored form. Rewrite the fraction \frac{x-3}{\left(x^2+9\right)\left(x+2\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{1}{13}x+\frac{3}{13}}{x^2+9}+\frac{5}{52\left(x+2\right)}+\frac{-1}{52\left(x-2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-\frac{1}{13}x+\frac{3}{13}}{x^2+9}dx results in: \frac{1}{13}\ln\left(\frac{3}{\sqrt{x^2+9}}\right)+\frac{1}{13}\arctan\left(\frac{x}{3}\right).

Find the integral int((x-3)/((x^2+9)(x^2-4)))dx