Learn how to solve integration by trigonometric substitution problems step by step online. Find the integral int((x^2+20x+-4)/((x-2)(x^2+4)))dx. Rewrite the fraction \frac{x^2+20x-4}{\left(x-2\right)\left(x^2+4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{5}{x-2}+\frac{-4x+12}{x^2+4}\right)dx into 2 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{-4x+12}{x^2+4}dx results in: 4\ln\left(\frac{2}{\sqrt{x^2+4}}\right)+6\arctan\left(\frac{x}{2}\right).

Find the integral int((x^2+20x+-4)/((x-2)(x^2+4)))dx