Exercise
$\int\frac{x^2-1}{x^3-x^2-2x}dx$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the integral int((x^2-1)/(x^3-x^2-2x))dx. Rewrite the expression \frac{x^2-1}{x^3-x^2-2x} inside the integral in factored form. Rewrite the expression \frac{x^2-1}{x\left(x-2\right)\left(x+1\right)} inside the integral in factored form. Rewrite the fraction \frac{x-1}{x\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x}+\frac{1}{2\left(x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral int((x^2-1)/(x^3-x^2-2x))dx
Final answer to the exercise
$\frac{1}{2}\ln\left|x\right|+\frac{1}{2}\ln\left|x-2\right|+C_0$