`int1/(x^2-4x+9)dx`
Let's complete the square for the denominator of the integral as:
`(x^2-4x+9)=(x-2)^2+5`
`(x-2)^2+(sqrt(5))^2`
`int1/(x^2-4x+9)dx=int1/((x-2)^2+(sqrt(5))^2)dx`
Let's apply the integral substitution,
substitute `u=x-2`
`du=1dx`
`=int1/(u^2+(sqrt(5))^2)du`
Now use the standard integral :`int1/(x^2+a^2)=1/aarctan(x/a)`
`=1/sqrt(5)arctan(u/sqrt(5))`
substitute back u=(x-2) and add a constant C to the solution,
`=1/sqrt(5)arctan((x-2)/sqrt(5))+C`
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