Style of latex formulas

Question

I have the given formula given in overleaf latex:

Given by

\begin{equation}
    H=\int \bigg(\big||\partial_x|^{\alpha/2}\psi\big|^2+\frac{1}{2}\big||\partial_x|^{-\beta/4}\psi\big|^4\bigg)dx
\end{equation}

However, I find this integral sign to be rather boring, compared to the nicer version:

How can I change this type of integration sign to be more like the lower picture?

Thanks

The preamble is:

\documentclass{article}
\usepackage{hyperref}
\usepackage{url}
\usepackage{enumerate}
\usepackage{rotating, graphicx}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{wrapfig}
\usepackage{setspace}
\usepackage{lscape}
\usepackage{rotating}
\usepackage{epstopdf}
\usepackage{MnSymbol}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage[table,xcdraw]{xcolor}
\usepackage{lscape}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage[mathscr]{euscript}
\usepackage{mathrsfs}
\usepackage{yfonts}
\usepackage{setspace}
\doublespacing
\usepackage{imakeidx}
\usepackage[colorinlistoftodos]{todonotes}

Answer 1

See, if the following example gives (similar) result what you after:

\documentclass{article}

\usepackage{nccmath,        % for \mfrac: medium size of \frac
            mathtools}      % it load amsmath too
\DeclarePairedDelimiter\abs{\lvert}{\rvert} % for writing absolute values
% instead of your "\newcommand{\norm}[1]{\left\lVert#1\right\rVert}"
\DeclarePairedDelimiterX\norm[1]\lVert\rVert{\ifblank{#1}{{\cdot}}{#1}} 
\usepackage{esint}          % new, for integrals
\usepackage{derivative}     % new, for commands for writing derivatives in a straightforward manner

\begin{document}
        \begin{equation}
H = \int \biggl(\abs*{\abs{\partial_x}^{\alpha/2} \psi}^2
        + \mfrac{1}{2}\abs*{\abs{\partial_x}^{-\beta/4}\psi}^4\biggr)\odif{x}
    \end{equation}
\end{document}

Off topic:
In your preamble many packages are loaded twice, some of them (like utf8, etc) are at newes LaTeX version not needed anymore.

\documentclass{article}
\usepackage{hyperref}           % should be last in reamble
%\usepackage{url}               % loaded by hyperref
\usepackage{enumerate}
\usepackage{rotating, graphicx}
\usepackage{amsmath}            % loaded by mathtools
\usepackage{amssymb}
\usepackage{wrapfig}
\usepackage{setspace}
\usepackage{lscape}
%\usepackage{rotating}          % loaded second time
\usepackage{epstopdf}           % not needed anymore, covered by graphicx
%\usepackage{MnSymbol}          % you not liked its integral signs
\usepackage[utf8]{inputenc}
\usepackage{amsmath}            % loaded second time
\usepackage[table,xcdraw]{xcolor}
\usepackage{lscape}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage[mathscr]{euscript}  % is really need?
\usepackage{mathrsfs}           % is really need?
\usepackage{yfonts}             % is really need?
\usepackage{setspace}           % loaded second time
\doublespacing
\usepackage{imakeidx}
\usepackage[colorinlistoftodos]{todonotes}