Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- 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 $3x^2+2$ by $x-1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}3x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-3x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{2}+3x\phantom{;};}\phantom{;}3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;-3x\phantom{;}+3\phantom{;}\phantom{;}-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((3x^2+2)/(x-1))dx. Divide 3x^2+2 by x-1. Resulting polynomial. Expand the integral \int\left(3x+3+\frac{5}{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{5}{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.