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Integrable?

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

Note by Tanishq Varshney
10 months, 2 weeks ago

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What makes you think it has a closed form? · 10 months, 2 weeks ago

Actually while solving one of the question , my mistake yielded this, so I checked it on wolfram alpha and it gave me an answer. · 10 months, 2 weeks ago

You didn't answer my question: is there a closed form? · 10 months, 2 weeks ago

I couldn't find it , probability of finding its closed form is 1/2 ;). · 10 months, 2 weeks ago

Can you at least tell where/how you form this integral? · 10 months, 2 weeks ago

The simplest form I can find is $$\displaystyle 2 \sum_{n=0}^\infty \dfrac{ (-1)^n (2n)!!}{(2n+1)(2n+1)!!}$$. · 10 months, 2 weeks ago