Write a value of `intsqrt(x^2-9)\ dx`

Explanation

Solution:

`I=\int \sqrt{x^{2}-9} d x` This is of the form

`\int \sqrt{x^{2}-a^{2}} d x`

We know that `\int \sqrt{x^{2}-a^{2}} d x=\frac{x}{2} \sqrt{x^{2}-a^{2}}-\frac{a^{2}}{2} \log \|x+\sqrt{x^{2}-a^{2}} |+c`

Replace `a \rightarrow 3`

`\therefore I=\frac{x}{2} \sqrt{x^{2}-3^{2}}-\frac{3^{2}}{2} \log \|x+\sqrt{x^{2}-3^{2}} |+c`

=`\frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \log \|x+\sqrt{x^{2}-9}|+c`