Math challenge N 3 : calculate this integral

A new challenge for people who love math and for intelligent man.
we have here a difucult exercise with one solution so I challenge you to solve the exercise with another way without using mapple mathimatica ...

So the deal here is just to be in the cercle of math especially with students and people who have a background in math, and of coursr improve ours skills ...

Here is the exercise :

the question is calculate this integral :

Here is solution

part 1 :

part 2 :

Finally I hope you enjoy with that article.