\[ \int \frac{x+3}{\sqrt{4 x^{2}+4 x-3}} d x=\frac{1}{4} \sqrt{f(x)...

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\[
\int \frac{x+3}{\sqrt{4 x^{2}+4 x-3}} d x=\frac{1}{4} \sqrt{f(x)}
\]
\( \mathrm{P}^{120} \)
W
\( +\frac{5}{2} \int \frac{d x}{\sqrt{4 x^{2}+4 x-3}} \), then find the minimum
value of \( f(x) \).
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