Let a, b, c be real numbers such that a≥b≥c≥1.
Prove the following inequality:
\int_0^1 \{(1\minus{}ax)^3\plus{}(1\minus{}bx)^3\plus{}(1\minus{}cx)^3\minus{}3x\}\ dx\geq ab\plus{}bc\plus{}ca\minus{}\frac 32(a\plus{}b\plus{}c)\minus{}\frac 34abc. calculusintegrationinequalitiescalculus computations