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

Question

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

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Answer

$\int\sqrt{9+\text{x}^2}\text{ dx}$
$=\int\sqrt{3^2+\text{x}^2}\text{ dx}$ $\Big(\because\sqrt{\text{a}^2+\text{x}^2}=\frac{\text{x}}{2}\sqrt{\text{x}^2+\text{a}^2}+\frac{\text{a}^2}{2}\ln\Big|\text{x}+\sqrt{\text{x}^2+\text{a}^2}\Big|\Big)$
$=\frac{\text{x}}{2}\sqrt{9+\text{x}^2}+\frac{9}{2}\ln\Big|\text{x}+\sqrt{9+\text{x}^2}\Big|+\text{C}$

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