Learn how to solve problems step by step online. Find the integral int((x^2+1)/((x-2)(x-3)^2))dx. Rewrite the fraction \frac{x^2+1}{\left(x-2\right)\left(x-3\right)^2} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{5}{x-2}+\frac{10}{\left(x-3\right)^2}+\frac{-4}{x-3}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{5}{x-2}dx results in: 5\ln\left(x-2\right). The integral \int\frac{10}{\left(x-3\right)^2}dx results in: \frac{-10}{x-3}.

Find the integral int((x^2+1)/((x-2)(x-3)^2))dx