Write a value of x^2-9 dx - Vidyadip

Question

Write a value of $\int\sqrt{\text{x}^2-9}\text{ dx}$

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Answer

Let $\text{I}=\int\sqrt{\text{x}^2-9}\text{ dx}$
We know that,
$\int\sqrt{\text{x}^2-\text{a}^2}\text{ dx}=\frac{\text{x}}{2}\sqrt{\text{x}^2-\text{a}^2}-\frac{\text{a}^2}{2}\log\Big|\text{x}+\sqrt{\text{x}^2-\text{a}^2}\Big|+\text{C}$
Here $a = 3, a^2 = 9$
$\therefore\ \text{I}=\frac{\text{x}}{2}\sqrt{\text{x}^2-9}-\frac{9}{2}\log\Big|\text{x}+\sqrt{\text{x}^2+9}\Big|+\text{C}$

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