Find the following integrals in Exercises: ^2 (1-1 x^2 )dx - Vidyadip

Question

Find the following integrals in Exercises:
$\int\text{x}^2 \bigg(1-\frac{1}{\text{x}^2}\bigg)\text{dx}$

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Answer

$\int\text{x}^2 \bigg(1-\frac{1}{\text{x}^2}\bigg)\text{dx}=\int\bigg(\text{x}^2-\frac{\text{x}^2}{\text{x}^2}\bigg)\text {dx}$
$=\int(\text{x}^2-1)\text{dx}=\int\text{x}^2\text{ dx}-\int1\text{ dx}$
$\frac{\text{x}^3}{3}-\text{x+c}\ \ \ \ \ \ \ \ \ \ \ \bigg[\because\int\text{x}^\text{n} \text{ dx}=\frac{\text {x}^{\text{n}+1}}{\text{n+1}}\text{ if}\text{ n}\neq-1\bigg]$

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