Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the indefinite integral $\displaystyle \int \frac{1}{\sqrt{1+(4 x - 6)^2}}\, dx$

Then the most appropriate substitution to simplify this integral is $x = g(t)$ where
$g(t)$ =
Note: We are using $t$ as variable for angles instead of $\theta$, since there is no standard way to type $\theta$ on a computer keyboard.

After making this substitution and simplifying (using trig identities), we obtain the integral $\displaystyle \int f(t)\,dt$ where
$f(t)$ =

This integrates to the following function of $t$
$\displaystyle \int f(t)\,dt$ = $+ C$
After substituting back for $t$ in terms of $x$ we obtain the following final form of the answer:
$+ C$