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

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