MHB Integral of sine = 27/2+ln^2(2)+ln(2)

[Tony1]

How to prove this integral,

$$\int_{0}^{2\pi}\sin\left({x\over 2}\right)\ln^2\left[\sin\left({x\over 4}\right)\sin\left({x\over 8}\right)\right]={27\over 2}+\ln^2(2)+\ln(2)$$

 

[topsquark]

How to prove this integral,

$$\int_{0}^{2\pi}\sin\left({x\over 2}\right)\ln^2\left[\sin\left({x\over 4}\right)\sin\left({x\over 8}\right)\right]={27\over 2}+\ln^2(2)+\ln(2)$$

Where are you getting these monstrosities from?

-Dan

 

[Greg]

Hi Tony and welcome to MHB! :D

Why are you posting these problems? Also, do you have the solutions?

I am considering moving them to the "Challenge Questions an Puzzles" forum and I can mark them as "Unsolved Challenges" if you do not have solutions.

Also, I encourage you to give more meaningful titles to your threads - I will be renaming several of them in the near future.

Good evening,

greg1313

 

[Tony1]

Hi Tony and welcome to MHB! :D

Why are you posting these problems? Also, do you have the solutions?

I am considering moving them to the "Challenge Questions an Puzzles" forum and I can mark them as "Unsolved Challenges" if you do not have solutions.

Also, I encourage you to give more meaningful titles to your threads - I will be renaming several of them in the near future.

Good evening,

greg1313

Hi greg1313,

No, I have no solution for them, that why I am posting them for a solution.