Final Answer
Step-by-step Solution
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Divide $2x^3+7x^2+2x+9$ by $2x+3$
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$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+3;}{\phantom{;}x^{2}+2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+3\overline{\smash{)}\phantom{;}2x^{3}+7x^{2}+2x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+3;}\underline{-2x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-3x^{2};}\phantom{;}4x^{2}+2x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n;}\underline{-4x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}-6x\phantom{;}-;x^n;}-4x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x\phantom{;}+6\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}15\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve 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. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.