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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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