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Let

a,\ b,\ c

be positive real numbers. Prove the following inequality. \int_1^e \frac {x^{a \plus{} b \plus{} c \minus{} 1}[2(a \plus{} b \plus{} c) \plus{} (c \plus{} 2a)x^{a \minus{} b} \plus{} (a \plus{} 2b)x^{b \minus{} c} \plus{} (b \plus{} 2c)x^{c \minus{} a} \plus{}(2a \plus{} b)x^{a \minus{} c} \plus{} (2b \plus{} c)x^{b \minus{} a} \plus{} (2c \plus{} a)x^{c \minus{} b}]}{(x^a \plus{} x^b)(x^b \plus{} x^c)(x^c \plus{} x^a)}\geq a \plus{} b \plus{} c. I have just posted 500 th post. Thank you for your cooperations, mathLinkers and AOPS users. I will keep posting afterwards. Japanese Communities Modeartor kunny

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