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`int (x^2 + 1)/(x^2 - 2x + 2)^2 dx` Evaluate the integral

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Let's evaluate the above integral by rewriting the integrand as,




Now again rewrite the second integral,



Now let's evaluate the above three integrals,


Let's use the integral substitution,

Let u=x-1,



The above can be evaluated using the standard integral,

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