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fricas
(1) -> realElementary sinh x

\label{eq1}\frac{{{{e}^{x}}^{2}}- 1}{2 \ {{e}^{x}}}(1)
Type: Expression(Integer)
fricas
realElementary cosh x

\label{eq2}\frac{{{{e}^{x}}^{2}}+ 1}{2 \ {{e}^{x}}}(2)
Type: Expression(Integer)

fricas
fix == rule
  a/(?b*exp(x)) == a/b*exp(-x)
Type: Void

fricas
simplify fix realElementary sinh x
fricas
Compiling body of rule fix to compute value of type RewriteRule(
      Integer,Integer,Expression(Integer))

\label{eq3}\frac{{{e}^{x}}-{{e}^{- x}}}{2}(3)
Type: Expression(Integer)
fricas
simplify fix realElementary cosh x

\label{eq4}\frac{{{e}^{x}}+{{e}^{- x}}}{2}(4)
Type: Expression(Integer)




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