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Today's calculation of Integral 737

Source: created by kunny

July 3, 2011
calculusintegrationlogarithmsgeometryinequalitiescalculus computations

Problem Statement

Let a, ba,\ b real numbers such that a>1, b>1.a>1,\ b>1. Prove the following inequality. ∫−11(1+b∣x∣1+ax+1+a∣x∣1+bx) dx<a+b+2\int_{-1}^1 \left(\frac{1+b^{|x|}}{1+a^{x}}+\frac{1+a^{|x|}}{1+b^{x}}\right)\ dx<a+b+2
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