# An integral for thought

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

#### Attachments

• integral.nb
4.8 KB · Views: 246

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
Homework Helper
Gold Member
Dearly Missed
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
Mentor
I was trying to approve the attachment, but my PC doesn't know what file type *.NB is. What application uses *.NB files?

Mathematica.

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:

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

Then the result is:1.66469

#### Attachments

• integral.pdf
30.7 KB · Views: 125
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