I need to calculate the following complex integral:

oint_C { [(z^4exp(2z)+1)/(z+i)^3] - [(z^3+z)/{(z-2i)(z-5)}] + 8*Pi*exp } dz,

Where C is the circumference |z-1| = sqrt(11/2), positively oriented.

Someone can help me, I already researched but I can not integrate.

Good evening,
I know the plot package and use frequently, but the basics. Now I need to make a curve that looks like an " umbrella " and it appears the projection in the xy plane . I don't know if it's possible , but I'm not getting . Does anyone have any idea to help me ? Thank you!

[Here's the original Question, restored as best I could.--Carl Love]

[The question was, of course, How to avoid the error?--Carl Love]

Download subgrouplattice_(1).mw