\[ \begin{array}{l} \int \frac{x+3}{\sqrt{4 x^{2}+4 x-3}} d x \\ =\...

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\[
\begin{array}{l}
\int \frac{x+3}{\sqrt{4 x^{2}+4 x-3}} d x \\
=\frac{1}{4} \sqrt{f(x)}+\frac{5}{2} \int \frac{d x}{\sqrt{4 x^{2}+4 x-3}} \text { then find }
\end{array}
\]
\( \mathrm{P}^{12} \)
W minimum value of \( f(x) \) ?
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