Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^2+x$ by $2x-1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}-1;}{\phantom{;}\frac{1}{2}x\phantom{;}+\frac{3}{4}\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}2x\phantom{;}-1;}\underline{-x^{2}+\frac{1}{2}x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+\frac{1}{2}x\phantom{;};}\phantom{;}\frac{3}{2}x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n;}\underline{-\frac{3}{2}x\phantom{;}+\frac{3}{4}\phantom{;}\phantom{;}}\\\phantom{;-\frac{3}{2}x\phantom{;}+\frac{3}{4}\phantom{;}\phantom{;}-;x^n;}\phantom{;}\frac{3}{4}\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+x)/(2x-1))dx. Divide x^2+x by 2x-1. Resulting polynomial. Expand the integral \int\left(\frac{1}{2}x+\frac{3}{4}+\frac{3}{4\left(2x-1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{3}{4\left(2x-1\right)}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 2x-1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.