Find the integral $\int\frac{3x-5}{\left(x-1\right)\left(x^2-1\right)}dx$

Got another answer? Verify it here!

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