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Integrable?

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

Note by Tanishq Varshney
1 year ago

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@Tanishq Varshney What makes you think it has a closed form? Pi Han Goh · 1 year ago

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@Pi Han Goh 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 · 1 year ago

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@Tanishq Varshney You didn't answer my question: is there a closed form? Pi Han Goh · 1 year ago

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

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@Tanishq Varshney Can you at least tell where/how you form this integral? Pi Han Goh · 1 year ago

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

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