Mathematics

Solve: $$\displaystyle \int \dfrac{x^3}{x - 2}dx$$


SOLUTION
$$\displaystyle\int \dfrac{x^3}{x-2}dx$$
$$=\displaystyle\int \left[\dfrac{(x-2)(x^2+2x+4)+8}{(x-2)}\right]dx$$
$$=\displaystyle\int \left[(x^2+2x+4)+\dfrac{8}{x-2}\right]dx$$
$$=\dfrac{x^3}{3}+x^2+4x+8 ln(x-2)+c$$
$$\therefore \displaystyle\int \dfrac{x^3}{x-2}dx=\dfrac{x^3}{3}+x^2+4x+8 ln(x-2)+c$$

           $$x^2+2x+4$$
$$x-2) x^3$$
       $$x^3-2x^3$$
       ________________
                $$2x^2$$
                $$2x^2-4x$$
               _____________
                          $$4x$$
                          $$4x-8$$
                         __________
                                 $$8$$.
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Subjective Medium Published on 17th 09, 2020
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