Chứng minh rằng :
a) $\int\limits_{0}^{\frac{\pi}{4} } \ln (1+\tan x ) dx \geq \frac{1}{2} \ln 2 $
b) $\int\limits_{0}^{1}x\ln (x + \sqrt{1+x^2})dx \geq \frac{1}{2} (1+\sqrt{2}) + \frac{\sqrt{2} }{2} -1$
c) $\frac{5 \pi }{6} < \int\limits_{\frac{\pi}{6} }^{\frac{\pi}{3} } ( 3 -2 \sqrt{\sin x})(5 + \sqrt{\sin x})( 1 +\sqrt{\sin x})dx < \frac{9\pi}{2}$
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