# Plotting a graph of a function that can't be solved in LaTeX (or wolframaplha)

I would like to plot a graph of this function:

Alternatively it could be expressed like this:

Either way, it's a symbolic expression, and as far as I'm aware, LaTeX can't solve it for me. Wolframalpha can't solve this either. Unfortunately, I don't have access to Mathematica to plot it.

Failing an exact plot of the function, I tried to simply capture its behaviour, as I know it should look similar to

The numbers on the axis and graph aren't important, I would simply like to be able to draw a graph like in the image. I can't think of a function that captures a similar behaviour however. Is there a way to literally draw a curve in LaTeX?

• Welcome to TeX.SE. Have you tried Matlab? It can solve numerically this type of equations. – Diaa Oct 10 '19 at 23:55
• Unfortunately I don't have that either, and I've already used the free trial. I suppose I can try to find someone with it, especially if it can solve the integral itself. – user1066 Oct 11 '19 at 0:27

Welcome! I am sure you can tweak the parameters to find an even better fit, but to very first approximation this is just a linear combination of two Gaussians of opposite signs, different amplitudes and widths (plus a shift by pi/2). You can play with the widths and prefactors to get a better fit.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}