Write a value

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 $\int x^{2}+9$

$=\int x^{2}+3^{2}$

$=\frac{x \sqrt{x^{2}+3^{2}}}{2}+\frac{3^{2}}{2} \log \left|x+\sqrt{x^{2}+3^{2}}\right|$

$=\frac{x \sqrt{x^{2}+9}}{2}+\frac{9}{2} \log \left|x+\sqrt{x^{2}+9}\right|+c$

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