Note: You can get full credit for this problem by just answering 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 $\int \frac{1}{3 x +7 \sqrt{x}}\, dx$

Then the most appropriate substitution to simplify this integral is
$u$ =

Then $dx = f(x)\,du$ where
$f(x)$ =

After making the substitution and simplifying we obtain the integral $\int g(u)\,du$ where
$g(u)$ =

This last integral is: = $+ C$
(Leave out constant of integration from your answer.)

After substituting back for $u$ we obtain the following final form of the answer:
= $+ C$
(Leave out constant of integration from your answer.)