Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^3-6x-20$ by $x+5$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{2}-5x\phantom{;}+19\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-6x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-5x^{2};}-5x^{2}-6x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{2}+25x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}+25x\phantom{;}-;x^n;}\phantom{;}19x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-19x\phantom{;}-95\phantom{;}\phantom{;}}\\\phantom{;;-19x\phantom{;}-95\phantom{;}\phantom{;}-;x^n-;x^n;}-115\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3-6x+-20)/(x+5))dx. Divide x^3-6x-20 by x+5. Resulting polynomial. Expand the integral \int\left(x^{2}-5x+19+\frac{-115}{x+5}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-115}{x+5}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+5 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.