Answer
$\dfrac{ x^2- x^{-2}}{2}$
Work Step by Step
Use the hyperbolic function formula as follows: $ \sinh x= \dfrac{e^x-e^{-x}}{2}$
Need to solve: $ \sinh ( 2 \ln x)$
$ \sinh ( 2 \ln x)= \dfrac{e^{2 \ln x}-e^{(- 2 \ln x})}{2} \\=\dfrac{e^{\ln x^2}-e^{(\ln x^{-2})}}{2} \\
=\dfrac{ x^2- x^{-2}}{2}$
