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question on how to solve this integration by quadratics

Mathematics
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can u complete the square in denominator ?
can you solve it using quadratics technique or would you do it using partial

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Other answers:

\(x^2-2x+2= (x-....)^2+...^2\)
when i tried quadratic equation i got (x-4)(x-2) which wouldnt work
ah (x-1)^2 would work too
(x-4)(x-2) ??? how ?
(x-1)^2 + 1^2 would work right
my bad what i meant was (x+2)(x-4)
but then you cant square it to use the quadratic stuff
(x-1)^2 + 1^2 would work right \(\checkmark \)
i think i got it from here i forgot you could split + 2 into another piece
put u = x-1 and use the standard formula for 1/ (x^2+a^2)
i had my mindset on adding stuff to make it right

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