Evaluate the following integrals: x^5+x^ -2 +2 x^2 dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{\text{x}^5+\text{x}^{-2}+2}{\text{x}^2}\text{dx}$

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Answer

$\int\frac{\text{x}^5+\text{x}^{-2}+2}{\text{x}^2}\text{dx}$
$=\int\bigg(\frac{\text{x}^5}{\text{x}^2}+\frac{\text{x}^{-2}}{\text{x}^2}+\frac{2}{\text{x}^2}\bigg)\text{dx}$
$=\int\text{x}^3\text{dx}+\int \text{x}^{-4}+2\int\text{x}^{-2}\text{dx}$
$=\frac{\text{x}^4}{4}+\frac{\text{x}^{-3}}{-3}+\frac{2\text{x}^{-1}}{-1}+\text{C}$
$=\frac{\text{x}^4}{4}-\frac{\text{x}^{-3}}{-3}-\frac{2}{\text{x}}+\text{C}$

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