Learn how to solve problems step by step online. Find the integral int((3x^3-8x^2+-10)/(x(x-1)^3))dx. Rewrite the fraction \frac{3x^3-8x^2-10}{x\left(x-1\right)^3} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{10}{x}+\frac{-15}{\left(x-1\right)^3}+\frac{-7}{x-1}+\frac{8}{\left(x-1\right)^{2}}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{10}{x}dx results in: 10\ln\left(x\right). The integral \int\frac{-15}{\left(x-1\right)^3}dx results in: \frac{15}{2\left(x-1\right)^{2}}.

Find the integral int((3x^3-8x^2+-10)/(x(x-1)^3))dx