I was thinking to solve some difficult integration problems and I came across this. This is too hard for me to do. I began to solve this as usual but I couldn't find a way to proceed. Please help and thanks in advance. $$\int_{0}^{\frac{\pi}2} \arccos\left(\frac{\cos x}{1+2\cos x}\right)dx=?$$
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1Do you know how to do the Ahmed's integral? – Laxmi Narayan Bhandari Oct 02 '21 at 09:54
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Actually i don't – Oct 02 '21 at 09:56
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Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Oct 02 '21 at 10:00
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1https://www.math.ucla.edu/~josephbreen/Some_Very_Challenging_Calculus_Problems-2.pdf see this – Zootopia Oct 02 '21 at 10:00
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the question you are asking is of UCLA – Zootopia Oct 02 '21 at 10:00
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https://math.stackexchange.com/questions/3966889/evaluate-and-explain-int-0-frac-pi2-arccos-left-frac-cos-x-left1 see this – Mariusz Iwaniuk Oct 02 '21 at 11:44
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This is a well known difficult integral called Coexter's integral which is also related to Ahmed's Integral. – Dharmendra Singh Oct 02 '21 at 14:50
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This question was closed for being a duplicate of another question, but the linked question is also closed. Shouldn’t at least one of q’s be open? – David H Oct 02 '21 at 19:27