If \( \int \frac{x \cos \alpha+1}{\left(x^{2}+2 x \cos \alpha+1\rig...

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If \( \int \frac{x \cos \alpha+1}{\left(x^{2}+2 x \cos \alpha+1\right)^{3 / 2}} d x=\frac{f(x)}{\sqrt{g(x)}}+C \) then find \( f(x) \) and \( g(x) \).
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