Mathematics

Find $$\displaystyle\int { \cfrac { { x }^{ 3 }-1 }{ { x }^{ 2 } }  } dx$$.


SOLUTION
Given $$\displaystyle\int{\dfrac{x^3-1}{x^2}dx}$$
$$=\displaystyle\int{\dfrac{x^3}{x^2}dx}-\int{\dfrac{1}{x^2}dx}$$
$$=\displaystyle\int{x dx}-\int{x^{-2}}$$
$$=\displaystyle\dfrac{x^2}{2}-\left(\dfrac{x^{-2+1}}{-2+1}\right)$$
$$=\dfrac{x^2}{2}+x^{-1}$$
$$=\dfrac{x^2}{2}+\dfrac{1}{x}+C$$
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Subjective Medium Published on 17th 09, 2020
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