Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^3$ by $x+2$
Learn how to solve differential equations problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}-2x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}+4x\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-4x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;-4x\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n;}-8\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve differential equations problems step by step online. Find the integral int((x^3)/(x+2))dx. Divide x^3 by x+2. Resulting polynomial. Expand the integral \int\left(x^{2}-2x+4+\frac{-8}{x+2}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-8}{x+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 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.