Evaluate x^3-1 x^2 dx - Vidyadip

Question

Evaluate $\int\frac{\text{x}^3-1}{\text{x}^2}\text{ dx}$

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Answer

$\int\Big(\frac{\text{x}^3-1}{\text{x}^2}\Big)\text{ dx}$
$=\int\Big(\frac{\text{x}^3}{\text{x}^2}-\frac{1}{\text{x}^2}\Big)\text{dx}$
$=\int(\text{x}-\text{x}^{-2})\text{dx}$
$=\frac{\text{x}^2}{2}-\frac{\text{x}^{-2+1}}{-2+1}+\text{C}$
$=\frac{\text{x}^2}{2}+\frac{1}{\text{x}}+\text{C}$

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