Learn how to solve integration by trigonometric substitution problems step by step online. Find the integral int((3-x)/(x(x^2+1)))dx. Rewrite the fraction \frac{3-x}{x\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{3}{x}+\frac{-3x-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{3}{x}dx results in: 3\ln\left(x\right). The integral \int\frac{-3x-1}{x^2+1}dx results in: -\frac{3}{2}\ln\left(x^2+1\right)-\arctan\left(x\right).

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