Present numerical results with variable system parameters I've been working on a problem where I ended up with a potential field expressed in terms of the following integral:
$$I(u)=\int_1^u \frac{e^{-x} (2 x-1)}{\sqrt{x~(A~e^{-x}+1)-B \sqrt{x}}}dx \,,$$
where $A,B\in \mathbb{R}$ are constants such that the integrand has no singularities.
The integral, unfortunately, can't be solved analytically so I was hopping to show the behavior of the potential in a plot. My problem are the constants $A$ and $B$ which represent some parameters of the system that I'm studying. How can I plot the function $I$? Should I make different plots for various values of the constants? Should I present one plot for various values of $A$ and fixed $B$ and vice-versa? I would be really grateful if someone could share their experience on how to best present such information.
 A: Because contour plots--especially 3D contour plots--are usually difficult to interpret and plots of $I$ against $u$ are familiar to physicists, consider a small multiple of such plots where $A$ and $B$ range through selected values.
Experimentation is in order.  You might, for instance, overlay multiple graphs for fixed $A$:

In each of these plots $B$ varies through the sequence $(-6, -1, 0, 1, 2)$ with color denoting the value of $B$; a legend would be helpful.  (The first value of $B$ is drawn in blue; the next values are drawn in red, gold, green, and so on.)
You could also overlay multiple graphs for fixed $B$:

In each of these plots $A$ varies through the sequence $(-2, 0, 2, 4, 6, 8)$.  Again, a legend would help.
Because these tableaux convey the same information in different ways, if space is available you might publish both versions.
Notice how, to assist visual comparison across the cells of each tableau, identical scales and ranges on the axes were used.  Sometimes values vary so much this is not feasible, in which case you need to draw the reader's attention to the changes in the scales.
Another thing worth considering is how, if at all, to standardize the plots.  It might be more meaningful physically, for instance, to scale them all so that the minimum $I(1/2)$ is equal to a constant value.  For other purposes you might standardize them to make their slopes at a distinguished value, such as $I^\prime(1) = 1/\left(\sqrt{e} \sqrt{A-e B+e}\right)$, equal to a constant.
A: What would be "typical" values? What would be extreme values? 
You can think of I as a function of three variables $I(u,A,B)$. Since $u, A, B \in \mathbb{R}$, it's not that easy to represent. You can either make a 1d plot of $I(u;A,B)$ vs $u$ for fixed values of $A$ and $B$, where you then have to take some representative values of $A$ and $B$. You could also make 2d color or contour plots where only $B$ is fixed, or only $A$, so you'd have $I(u,A;B)$.
One thing you can do for a 3d plot where the axis are for $u$, $A$ and $B$ would be a constant-value contour, i.e. make a 3d plot of the surface at which $I(u,A,B) = c$ for some constant $c$. 
