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[tex]\int\limits_{\pi/4}^{\pi/3}\frac{sinx + cosx}{/sqrt{3 + cosx}}dx[/tex]
[TEX]\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{sinx + cosx}{\sqrt{3 + cosx}}dx = \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{cosx + 3 + sinx - 3}{\sqrt{3 + cosx}}dx[/TEX]
[TEX]\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\sqrt{3 + cosx}}dx + \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{sinxdx}{\sqrt{3 + cosx}} - \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{3dx}{\sqrt{3 + cosx}}[/TEX] :|
[TEX]I_1 = \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\sqrt{3 + cosx}}dx =\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\sqrt{4 - 2sin^2{\frac{x}{2}}}dx[/TEX]
[TEX]I_2 = \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{sinxdx}{\sqrt{3 + cosx}} = \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{-dcosx}{\sqrt{3 + cosx}}[/TEX]
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[TEX] I_3 = \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{3dx}{\sqrt{3 + cosx}} = 3\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}}{\frac{dx}{\sqrt{4 - 2sin^2{\frac{x}{2}}}}[/TEX]
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