I am interested in holding an Integration Contest here on Brilliant.org like any other online forums such as AoPS or Integrals and Series. The aims of the Integration Contest are to improve skills in the computation of integrals, to learn from each other as much as possible, and of course to have fun. Anyone here may participate in this contest.
The rules are as follows
- I will start by posting the first problem. If there is a user solves it, then (s)he must post a new one.
- You may only post a solution of the problem below the thread of problem and post your proposed problem in a new thread. Put them separately.
- Please make a substantial comment.
- Make sure you know how to solve your own problem before posting it in case there is no one can answer it within a week, then you must post the solution and you have a right to post another problem.
- If the one who solves the last problem does not post his/her own problem after solving it within a day, then the one who has a right to post a problem is the last solver before him/her.
- The scope of questions is only computation of integrals either definite or indefinite integrals.
- You are NOT allowed to post a multiple integrals problem as well as a complex integral problem.
- You are also NOT allowed to post a solution using a contour integration or residue method.
- The final answer can ONLY contain the following special functions: gamma function, beta function, Riemann zeta function, Dirichlet eta function, dilogarithm, digamma function, and trigonometric integral.
Please post your solution and your proposed problem in a single new thread.
Format your post is as follows:
SOLUTION OF PROBLEM xxx (number of problem) :
[Post your solution here]
PROBLEM xxx (number of problem) :
[Post your problem here]
Please share this note so that lots of users here know this contest and take part in it. (>‿◠)✌
Okay, let the contest begin! Here is the first problem:
PROBLEM 1 :
For , show that
P.S. You may also want to see Brilliant Integration Contest - Season 1 (Part 2) and Brilliant Integration Contest - Season 1 (Part 3).