Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $3x^2+3$ by $x-1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}3x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-3x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{2}+3x\phantom{;};}\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;-3x\phantom{;}+3\phantom{;}\phantom{;}-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((3x^2+3)/(x-1))dx. Divide 3x^2+3 by x-1. Resulting polynomial. Expand the integral \int\left(3x+3+\frac{6}{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{6}{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.