Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $2x^3+7x^2+2x+9$ by $2x+3$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+3;}{\phantom{;}x^{2}+2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+3\overline{\smash{)}\phantom{;}2x^{3}+7x^{2}+2x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+3;}\underline{-2x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-3x^{2};}\phantom{;}4x^{2}+2x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n;}\underline{-4x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}-6x\phantom{;}-;x^n;}-4x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x\phantom{;}+6\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}15\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x^3+7x^22x+9)/(2x+3))dx. Divide 2x^3+7x^2+2x+9 by 2x+3. Resulting polynomial. Expand the integral \int\left(x^{2}+2x-2+\frac{15}{2x+3}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{15}{2x+3}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 2x+3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.