Evaluate: `intsqrt(9-x^2)\ dx`

Explanation

`I=int sqrt{9+x^{2}} d x`


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

Replace `x rightarrow x and a rightarrow 3 `we get
`

int sqrt{3^{2}+x^{2}} d x =frac{x}{2} sqrt{3^{2}-x^{2}}+frac{3^{2}}{2} log |x+sqrt{x^{2}+3^{2}}|+c `
`
=frac{x}{2} sqrt{9-x^{2}}+frac{9}{2} log |x+sqrt{x^{2}+9}|+c`
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