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\[\large{\displaystyle \int ^{\frac{\pi}{2}}_{0} \arccos (\tan \left(\frac{x}{2}\right)) dx}\]

Note by Tanishq Varshney 1 year, 11 months ago

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@Pi Han Goh @Kartik Sharma @Ishan Singh

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What makes you think it has a closed form?

Actually while solving one of the question , my mistake yielded this, so I checked it on wolfram alpha and it gave me an answer.

@Tanishq Varshney – You didn't answer my question: is there a closed form?

@Pi Han Goh – I couldn't find it , probability of finding its closed form is 1/2 ;).

@Tanishq Varshney – Can you at least tell where/how you form this integral?

@Tanishq Varshney – The simplest form I can find is \( \displaystyle 2 \sum_{n=0}^\infty \dfrac{ (-1)^n (2n)!!}{(2n+1)(2n+1)!!} \).

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TopNewest@Pi Han Goh @Kartik Sharma @Ishan Singh

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What makes you think it has a closed form?

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Actually while solving one of the question , my mistake yielded this, so I checked it on wolfram alpha and it gave me an answer.

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