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[TEX]u = \sqrt{x^2+4} \\ u^2 = x^2+4 \\ x^2 = u^2-4 \\ 2xdx = 2udu \\ \int_{\sqrt{5}}^{2.\sqrt{3}}.\frac{x.dx}{x^2.\sqrt{x^2+4}} = \int_{3}^{4}\frac{u.du}{(u^2-4).u} \\ \int_{3}^{4}\frac{du}{(u-2)(u+2)} = \int_{3}^{4}\frac{1}{4}.[\frac{1}{u-2}- \frac{1}{u+2}] = \frac{1}{4}.ln |\frac{u-2}{u+2}| = \frac{1}{4}.ln (\frac{5}{3})[/TEX]