Help with Explicit Integral could not be found

Greetings everyone,

I've had this problem with Matlab a couple of times, where it says : Warning : Explicit integral could not be found. I've read that in order to avoid this message I should solve the integral numerically. Problem is, I don't have any values for my integral (It's a transport phenomena exercice). Here's the code bellow, if anyone can tell me what I'm doing wrong, that'd be awesome.

syms Vz r R k P0 Pl L landa n dvz
M1 = ((P0-Pl)*R)/(2*L);
M2 = (r/R)-(landa*landa*(R/r));
dvz= -(M1*M2)^(1/n);
Vz = int((dvz),r);

I'm trying to have the unsolved integral in order to keep on doing my problem.

Thanks!

Answer 1

[Walter Roberson]

You aren't doing anything wrong in terms of finding the integral (I cannot say whether your expressions are correct). The form simply doesn't have a closed-form integral within the constraints you have presented (which is to say, no constraints.) Possibly there is a set of constraints that would allow a closed form -- but I was not able to come up with one.

[Arthur]

Is there any way to tell MatLab not to consider the point n=0? I think that's why he won't give me an answer, due to the 1/n (division by zero).

In any case, thank you for your time.

[Walter Roberson]

No, n=0 is not the problem.

When n is an odd positive integer there appears to be a solution involving Legendre, but not for even integers from 4 up

When n is a positive rational, there are some fractions that work out using Legendre and there are some that do not. For example 11/3 works and 11/5 works but not 11/4. It is not as easy as "even denominators do not work" because 11/12 works.