How to avoid Singularity in numirical integration

I want to numerically integrate the following with Matlab:

fun=@(t) (((1 - (-1)^n*cos(n*pi*t/R)))./t);

hn = integral(fun,0,(sqrt(R^2-x^2)));

For now, I just avoided to evaluate the integral in 0, are they any way to encounter the singularity at this point.

Thank you.

Answer 1

[Raynier Suresh]

The “quadgk” function can handle singularity if the singularity is present at the boundary. In case if your singularity is not at the boundary you can split the integration domain to place the singularity at the boundary. Refer to the below links for more information,

Quadgk: https://www.mathworks.com/help/matlab/ref/quadgk.html#References

Split integration domain: https://www.mathworks.com/help/matlab/math/singularity-on-interior-of-integration-domain.html

[ABDEL MOUMEN]

Thank you Mr. Raynier Suresh