Getting "reached maximum number of intervals in use" error message on simple integration

I am trying to do a simple intergration, but am getting the "Reached maximum number of intervals in use" error message and the wrong answer:

This is the code:

fun=@(x) 1./(5 - x.^4)

answer = integral(fun,-10,10)

The answer should be 0.47

Answer 1

[Walter Roberson]

your function has discontinuities at +/- 1.495, which is within the range of integration. Numeric integration is not able to resolve the value.

[Matthew Chadder]

is there a way to avoid this issue?

[Walter Roberson]

No, it is not a removable discontinuity. There function goes to +infinity from the left near 5^(1/4) and to -infinity from the right near 5^(1/4) .

If you examine the interval int(1/(5-x^4), 5^(1/4)-2*10^(-N), 5^(1/4)-10^(-N)) and take the limit as N -> infinity, then Maple says it is 5^(1/4)*ln(2)/20 -- so from 10^(-1001) to 10^(-1000) there is an area about 0.052, from 10^(-1001) to 10^(-1002) there is an area of about 0.052, and so on. And there are an infinite number of these, so the area must approach infinity * 0.052, which would be infinite.

Then you get the same thing on the other side of the discontinuity, except with negative sign. So you have infinity - infinity which is not defined.