Question:
Write a value of $\int \sqrt{9+x^{2}} d x$.
Solution:
we know that $\int \sqrt{x^{2}+a^{2}} d x=\frac{x \sqrt{x^{2}-a^{2}}}{2}+\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}+a^{2}}\right|+c \mid$
Given $\int x^{2}+9$
$=\int x^{2}+3^{2}$
$=\frac{x \sqrt{x^{2}+3^{2}}}{2}+\frac{3^{2}}{2} \log \left|x+\sqrt{x^{2}+3^{2}}\right|$
$=\frac{x \sqrt{x^{2}+9}}{2}+\frac{9}{2} \log \left|x+\sqrt{x^{2}+9}\right|+c$