Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^2+2x$ by $x+1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}-x\phantom{;};}\phantom{;}x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;-x\phantom{;}-1\phantom{;}\phantom{;}-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+2x)/(x+1))dx. Divide x^2+2x by x+1. Resulting polynomial. Expand the integral \int\left(x+1+\frac{-1}{x+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-1}{x+1}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+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.