Final Answer
Step-by-step Solution
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Divide $2x^3+6x^2-26x-54$ by $x^2+2x-15$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}+2x\phantom{;}-15;}{\phantom{;}2x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2x\phantom{;}-15\overline{\smash{)}\phantom{;}2x^{3}+6x^{2}-26x\phantom{;}-54\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-15;}\underline{-2x^{3}-4x^{2}+30x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}-4x^{2}+30x\phantom{;};}\phantom{;}2x^{2}+4x\phantom{;}-54\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-15-;x^n;}\underline{-2x^{2}-4x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{;-2x^{2}-4x\phantom{;}+30\phantom{;}\phantom{;}-;x^n;}-24\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((2x^3+6x^2-26x+-54)/(x^2+2x+-15))dx. Divide 2x^3+6x^2-26x-54 by x^2+2x-15. Resulting polynomial. Expand the integral \int\left(2x+2+\frac{-24}{x^2+2x-15}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2xdx results in: x^2.