Improving Formatting For Math Assignment

I am fairly new to using LaTeX to typeset my math homework and I am having some troubles just doing some basic formatting. Ideally what I would like to have is the problem statement, in this case it would be A) in line with "Problem 1" and then work on the problem below it. That way my TA would be able to zip through the assignment quickly to distinguish which questions need to be marked (he marks them randomly for everybody). If there are any suggestions on how I could make this adjustment for better presentation, that would be welcomed.

documentclass[fleqn, 12pt]{article}
usepackage[utf8]{inputenc}
usepackage[margin=1in]{geometry}
usepackage{gensymb} % 
usepackage{amsmath}
usepackage{amssymb} 
usepackage{stmaryrd}
usepackage[shortlabels]{enumitem}


 
begin{document}

maketitle

section*{Problem 1}
begin{equation*}
    text{A)} quad int{frac{cos t}{(1 + sin t)^{frac{1}{2}} } , dx}
end{equation*}

quad Let $ u = 1 + sin t$ and $ frac{, du}{, dt} = cos t $ and, by substitution, we get:
begin{equation}
    int{ frac{1}{sqrt{u}} , du} = 2sqrt{u} + C
end{equation}

section*{Problem 2}

section*{Problem 3}

end{document}