Mathematics

Evaluate
$$\displaystyle\int { \dfrac { { x }^{ 3 }+{ 4x }^{ 2 }-7x+5 }{ x+2 }  } dx$$


SOLUTION
$$\displaystyle\int \dfrac{x^3+4x^2-7x+5}{x+2}dx$$

         $$x^2+2x-11$$
         ________________
$$x+2)x^3+4x^2-7x+5$$
          $$x^3+2x^2$$
         ________________
                 $$2x^2-7x$$
                 $$2x^2-4x$$
               ______________
                           $$-11x+5$$
                           $$-11x-22$$
                          ____________
                                         $$27$$
                           ____________

So $$\displaystyle\int x^2+2x-11+\dfrac{27}{x+2}dx$$

$$\Rightarrow\dfrac{x^3}{3}+\dfrac{2x^2}{2}-11x+27 log(x+2)+c$$

$$\Rightarrow\dfrac{x^3}{3}+x^2-11x+27 log(x+2)+c$$.
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Subjective Medium Published on 17th 09, 2020
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