Answer
$\dfrac{ x^2- x^{-2}}{2}$
Work Step by Step
Use formula: $ \sinh x= \dfrac{e^x-e^{-x}}{2}$
Thus, $ \sinh ( 2 \ln x)= \dfrac{e^{2 \ln x}-e^{- 2 \ln x}}{2}=\dfrac{e^{\ln x^2}-e^{\ln x^{-2}}}{2}$
Hence, $ \sinh ( 2 \ln x)=\dfrac{ x^2- x^{-2}}{2}$
