Chứng minh rằng :
a) $ \int\limits_{0}^{\frac{\pi}{4} } \ln (1+ \tan x) dx \leq \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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