Learn how to solve combining like terms problems step by step online. Integrate the function (-9x-2)/((x+4)(x^2+1)) from 1 to infinity. Rewrite the fraction \frac{-9x-2}{\left(x+4\right)\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{x+4}+\frac{-2x-1}{x^2+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x+4}dx results in: 2\ln\left(x+4\right). The integral \int\frac{-2x-1}{x^2+1}dx results in: -\ln\left(x^2+1\right)-\arctan\left(x\right).

Integrate the function (-9x-2)/((x+4)(x^2+1)) from 1 to infinity