`int 1/(x^2-4x+9) dx` Find the indefinite integral

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Let's complete the square for the denominator of the integral as:




Let's apply the integral substitution,

substitute `u=x-2`



Now use the standard integral :`int1/(x^2+a^2)=1/aarctan(x/a)`


substitute back u=(x-2) and add a constant C to the solution,



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