I want to write an essay about one method that matlab uses to compute an approximation of integrals which include singularities as in:
$\int_{0}^{\infty }\frac{\sin (x^{5})}{x^{2}(1+x)^{55}}dx$
However after much research I haven't gotten much further due to the vast amount of different methods that can be used to approximate such an integral. I was hoping that one of you might know a method that can solve such integrals with a relatively high precision and is that is appropriate/interesting enough to write an essay on.
Regards,
Lorenzo