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