This problem concerns the integral$$xx$2+4$x$+13$dx$,$which can be solved using various methods. Show how to solve it using a trigonometric substitution, by completing the steps below.

$($a$)$ This integral can be evaluated using a single trigonometric substitution, which can be written in the form x$=$h$($t$),$ where

h$($t$)=.$

$($b$)$ Applying the substitution in $($a$)$ and simplifying leads to$$xx$2+4$x$+13$dx$=$g$($t$)$dt$,$where g$($t$)=.$

$($c$)$ Evaluate $$g$($t$)$dt:

$$g$($t$)$dt $=.$

$($d$)$ Finally, solve the original integral:

$$xx$2+4$x$+13$dx $=$