An integral for thought

[natski]

I am trying to integrate:

x(z)/(1+x(z)) wrt z.

I know the function x(z), it basically just made up a linear combination of several decimal powers of z. Mathematica refuses to do an numerical integration and just crashes when it gets a couple of minutes in on my laptop.

If x(z) was just z then I could obviously use some standard integrals but I think this is more complex than that. Any ideas on how to solve this one? I have attached the exact equation in a mathematica notebook.

Natski

 

[gonzo]

Is this complex or real integration? And what are your limits of integration? And it would probably help if you wrote out the entire integral.

 

[arildno]

Remember that this can effectively be reduced to integrating:
$$\int\frac{dz}{1+x(z)}$$
It is by no means obvious why this should at all be possible; if it were, you would for example be able to solve for the particular choice:
$$x(z)=e^{z^{2}}-1$$
That would be equivalent to find an anti-derivative to the error function..

 

[berkeman]

I was trying to approve the attachment, but my PC doesn't know what file type *.NB is. What application uses *.NB files?

 

[Eighty]

Mathematica.

 

[Crosson]

I posted the original content of the .nb file to the attached pdf. Maybe the forum needs a tutorial on the simple process for Mathematica -> TeX.

From a mathematica point of view, you natski are not integrating numerically, you are forcing a symbolic result. To integrate numerically, just use the function NIntegrate, like this:

NIntegrate[integrand, {ψ, 0, N[Pi/2]}]

Then the result is:1.66469