Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^2-2x-1$ by $x-2$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{2}-2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+2x\phantom{;};}-1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2-2x+-1)/(x-2))dx. Divide x^2-2x-1 by x-2. Resulting polynomial. Expand the integral \int\left(x+\frac{-1}{x-2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-1}{x-2}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x-2 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.