\(\frac{\mathscr{L}}{\frac{\rho_{\infty} V_{\infty}^{2} c}{2}}=\int_{0}^{\frac{b}{2}}\left(\frac{\partial C_{l}}{\partial \alpha}\left(\alpha-\alpha_{C_{l}=0}\right)+\frac{\partial C_{l}}{\partial \alpha} \varphi(v)-\frac{\partial C_{l}}{\partial \alpha} \frac{\dot{p} v}{V_{\infty}}+\frac{\partial C_{l}}{\partial \beta} \beta \mathscr{U}_{b_{2}}(v)\right) v d v\)
substitute this value in the integral and solve:
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