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Today's calculation of Integral 335

Source: 1994 Hiroshima University entrance exam

June 7, 2008
calculusintegrationlogarithmsinequalitiesfunctionderivativecalculus computations

Problem Statement

For t>0 t>0, prove that 12t∫t3txln⁡x dx≥2tln⁡2t \frac{1}{2t}\int_t^{3t} x\ln x\ dx\geq 2t\ln 2t.
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