Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $y^2$ by $y^2+6y+12$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}y^{2}+6y\phantom{;}+12;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}y^{2}+6y\phantom{;}+12\overline{\smash{)}\phantom{;}y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}y^{2}+6y\phantom{;}+12;}\underline{-y^{2}-6y\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{-y^{2}-6y\phantom{;}-12\phantom{;}\phantom{;};}-6y\phantom{;}-12\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((y^2)/(y^2+6y+12))dy. Divide y^2 by y^2+6y+12. Resulting polynomial. Expand the integral \int\left(1+\frac{-6y-12}{y^2+6y+12}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dy results in: y.