Final answer to the problem
Step-by-step Solution
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Divide $x^2+2$ by $x+2$
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$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}-2x\phantom{;};}-2x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x\phantom{;}+4\phantom{;}\phantom{;}-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((x^2+2)/(x+2))dx. Divide x^2+2 by x+2. Resulting polynomial. Expand the integral \int\left(x-2+\frac{6}{x+2}\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+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.