Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- Integrate by partial fractions
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Divide $x^3$ by $2x-1$
Learn how to solve 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 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. We can solve the integral \int\frac{1}{8\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.