An integral solved by Residue Theorem

[@scrumptiousjimmy9196]

Awesome video and explanation! I was trying to find how to handle a non-even power of x in the denominator and your strategy was excellent!

[@omargaber3122]

Greet wonderful ,thank you very much ❤️

[@MikeMagTech]

I just discovered your channel and subscribed.

[@ArifSolvesIt]

thank you very much. I have also started posting these videos very recently. I hope I will be able to create more videos that you will like in the near future. Best, Arif

[@ajokaefi]

You are a very goooood teacher!

[@ArifSolvesIt]

thanks a lot for your kind comment.

[@Mathin3D]

sum of cubes, partial fraction decomposition works.

[@ArifSolvesIt]

yes, that's right. I also solved it that way while solving a different integral: kzbin.info/www/bejne/rYCll5KDp7aJhNE another method is to make use of the beta and gamma functions, but I don't have a video on that.

[@MONKEYDLUFFY-tv3zw]

Thank You Professor

[@ArifSolvesIt]

It is my pleasure :-)

[@soneriftar]

this is a postgraduate-level mathematics subject and requires a solid background to understand. otherwise you only memorize the method and use only in exams. math without an engineering applications is torture.

thanks a lot

[@ArifSolvesIt]

You are most welcome

[@sergeyromanov2116]

Beautiful. How does one choose the contour?

[@ArifSolvesIt]

thanks a lot for your comment. It really depends on the problem. The main idea here is to be able to get an equation of the original integral of the problem. In the contour integral, you try to write it as the sum of the residues of the poles and a constant multiple of the original integral.

[@littlebuilders7287]

Great , why we didn’t take the upper half of the semi circle?

[@wei-hauchang2910]

Wow!

[@najeebullah9658]

Is the contour laying one point sir but what about the quadrant thirds sir

[@nakhleasmar9175]

Nice proof, but you need to justify that the middle integral goes to zero when the integrand goes to zero. This is not true in general. In this case, it's a very simple application of something called the ML-inequality.

[@ArifSolvesIt]

yes, you are right. I skipped that part little bit. The mathematics rigor requires those proofs definitely. However, for the integral we solved it was little bit too much obvious. But as you mentioned, it is not always the case.