kevin lucas on Fri, 16 Mar 2018 16:35:28 +0100


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Integration Methods in PARI


I have been trying to evaluate the following integral in PARI:

intnum(x=0, +oo, x*exp(cos(x))*sin(sin(x))/(x^2-1))

but end up with the following error

 ***   at top-level: ...x*exp(cos(x))*sin(sin(x))/(x^2-1))
 ***                                             ^---------
 *** _/_: impossible inverse in divrr: 0.E-230.
 ***   Break loop: type 'break' to go back to GP prompt


How should I proceed? More generally, how should one integrate such functions, which are oscillatory but not decomposable into a product of a non-oscillating function and a sine or cosine, as in the manual?

Any suggestions or references would be appreciated.

Lucas.