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Question
Find: `int (dx)/(x^2 - 6x + 13)`
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Solution
Given integral is I = `int (dx)/(x^2 - 6x + 13)`
= `int (dx)/((x - 3)^2 + 13 - 9)`
= `int (dx)/((x - 3)^2 + 4)`
= `int (dx)/((x - 3)^2 + 2^2)`
= `1/2 tan^-1 ((x - 3)/2) + C` ...`["Using" int 1/(x^2 + a^2) dx = 1/a tan^-1 x/a + C]`
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