Final Answer
Step-by-step Solution
Specify the solving method
Divide $3x^5-2x^3+5x^2-2$ by $x^3+1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{3}+1;}{\phantom{;}3x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{;}x^{3}+1\overline{\smash{)}\phantom{;}3x^{5}\phantom{-;x^n}-2x^{3}+5x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}+1;}\underline{-3x^{5}\phantom{-;x^n}\phantom{-;x^n}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{5}-3x^{2};}-2x^{3}+2x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}+1-;x^n;}\underline{\phantom{;}2x^{3}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{3}+2\phantom{;}\phantom{;}-;x^n;}\phantom{;}2x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((3x^5-2x^35x^2+-2)/(x^3+1))dx. Divide 3x^5-2x^3+5x^2-2 by x^3+1. Resulting polynomial. Simplify the expression inside the integral. We can solve the integral \int\frac{x^{2}}{x^3+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^3+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.