Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $5x^2+3$ by $x^2-2x-3$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}-3;}{\phantom{;}5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}-3\overline{\smash{)}\phantom{;}5x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-3;}\underline{-5x^{2}+10x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{-5x^{2}+10x\phantom{;}+15\phantom{;}\phantom{;};}\phantom{;}10x\phantom{;}+18\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((5x^2+3)/(x^2-2x+-3))dx. Divide 5x^2+3 by x^2-2x-3. Resulting polynomial. Expand the integral \int\left(5+\frac{10x+18}{x^2-2x-3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5dx results in: 5x.