Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^3$ by $2x-1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}-1;}{\phantom{;}\frac{1}{2}x^{2}+\frac{1}{4}x\phantom{;}+\frac{1}{8}\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}2x\phantom{;}-1;}\underline{-x^{3}+\frac{1}{2}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+\frac{1}{2}x^{2};}\phantom{;}\frac{1}{2}x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n;}\underline{-\frac{1}{2}x^{2}+\frac{1}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{;-\frac{1}{2}x^{2}+\frac{1}{4}x\phantom{;}-;x^n;}\phantom{;}\frac{1}{4}x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n-;x^n;}\underline{-\frac{1}{4}x\phantom{;}+\frac{1}{8}\phantom{;}\phantom{;}}\\\phantom{;;-\frac{1}{4}x\phantom{;}+\frac{1}{8}\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}\frac{1}{8}\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3)/(2x-1))dx. Divide x^3 by 2x-1. Resulting polynomial. Expand the integral \int\left(\frac{1}{2}x^{2}+\frac{1}{4}x+\frac{1}{8}+\frac{1}{8\left(2x-1\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2}x^{2}dx results in: \frac{1}{6}x^{3}.