Thread: Figuring out equivalent constants

Hello everyone,

I have two equations which are equal to the other, using undefined constants, and basically I would like help figuring out what the constants on the right-hand side are equal to in terms of the constants on the left hand side.
the equation is a little long and has lots of constants but is not too complicated:

a*b/(1+(b*x-c)^2) - d*e/(1+(e*x+f)^2) + g*i/(h-i*x) + j(2m*x-l)/(k-l*x+m*x^2) + n(p+2q*x)/(o+p*x+q*x^2) = r / (s/(t*x+u) - v*x^4)

[what are r, s, t, u and v equal to in terms of a-q]

math software?

thank you in advance if you can help, I'd appreciate it.

I assume that the equation should be true for all real x?



Two parameters at the right side are redundant. Apart from special cases, you can always set r=s=1, for example. In general, I would not expect that there are r,s,t,u,v to get both sides equal for all x.
Where does the equation come from?

Hello mfb,
This equation comes from the integration of the right expression, and since i couldn't do it manually I got the answer using Mathematica (not very good with it), but i wanted to know where the coefficients were coming from, so I thought the best way to proceed was to differentiate the integration so that the two sides would be equal.

using numbers this is the expression:
∫0.0024185/(2500/(0.485x+266)-8.3168 ×10^(-11) x^4 ) dx
=
-0.0821125 arctan(0.171695-0.00193589 x) - 0.0280283 arctan(0.00344281 x+2.10174)-0.0540371 ln(4.1169-0.00833949 x) +0.0181571 ln(0.0000695471 x^2-0.0123363x +19.1044)+0.00886143 ln( 0.0000695471x^2 +0.084913x+31.7859) + c

I'm doing this for a physics project, btw, so for a general equation i'd like to know where the coefficients end up after the integration.

sorry for the big muddle
[now i realize that in the first fraction it should actually be (c-bx)^2]

I would expect that Mathematica can give you the coefficients.
However, why do you want to express r,s,t,u,v in terms of the other parameters, if you already know them and need a-q?

[now i realize that in the first fraction it should actually be (c-bx)^2]

As you square it, the sign does not matter.

Using t=v=1 at the right side (you can always get this form), this can be written as
For a partial fraction decomposition, you would have to know the solutions of 0=s-ux^4-x^5, which should not have a closed form for arbitrary parameters s and u. In other words, I doubt that this integral can be solved in a meaningful way for all parameters.

r,s,t,u,v are variables that remain constant during the process i'm trying to describe, so i have values for them, but i'd like to be able to insert them in the arctan and log function and thus get a general equation.
But if you say it can't be done then that's too bad.

Hold on, I somehow managed to get an answer using the wolfram software. It is really complicated but it's something:



any opinion?

This looks like the case u=0, which is much simpler.
Instead of b/(cd), you can simplify the equation to set this to 1. This reduces the size of the solution.