Answer
$$G(v) =5v+3\tan v+C $$
Work Step by Step
Given $$g(v) = 5+ 3\sec^2v$$
Then by using table 2 if $f(x)= x^n\ \to\ \ F(x) = \frac{x^{n+1}}{n+1} +C$ and if
$f(x)=\sec^2x\ \to\ \ F(x) =\tan x +C$
Hence
\begin{align*}
G(v)&=5v+3\tan v+C
\end{align*}
To check
\begin{align*}
G'(v) &= 5+ 3\sec^2v\\
&=g(v)
\end{align*}
