Answer
$F(x)=\displaystyle \frac{2^{x}}{\ln 2}+4\cosh x+C$
Work Step by Step
From the Table of Antiderivatives,
$f(x)=b^{x}\displaystyle \quad \Rightarrow\quad F(x)=\frac{b^{x}}{\ln b}+C$
$f(x)=\sinh x\quad \Rightarrow\quad F(x)=\cosh x+C$
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$f(x)=2^{x}+4\sin h$
$F(x)=\displaystyle \frac{2^{x}}{\ln 2}+4\cosh x+C$