Note: You can get full credit for this problem by just entering the 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 $$\int\frac{4}{4+e^x}\,dx$$

The most appropriate substitution to simplify this integral is $u = f(x)$ where
$f(x)$ =

We then have $$dx = g(u)\,du$$ where
$g(u)$ =

Hint: you need to back substitute for $x$ in terms of $u$ for this part.

After substituting into the original integral we obtain $\displaystyle \int h(u)\, du$ where
$h(u)$ =

To evaluate this integral rewrite the numerator as $$4 = u - (u - 4)$$ simplify, then integrate, thus obtaining $$\int h(u)\, du = H(u)$$ where
$H(u)$ = + $C$

After substituting back for $u$ we obtain our final answer
$\displaystyle \int\frac{4}{4+e^x}\,dx$ = + $C$