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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, 11 months ago

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- 1 year, 11 months ago

What makes you think it has a closed form?

- 1 year, 11 months 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.

- 1 year, 11 months ago

You didn't answer my question: is there a closed form?

- 1 year, 11 months ago

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

- 1 year, 11 months ago

Can you at least tell where/how you form this integral?

- 1 year, 11 months ago

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

- 1 year, 11 months ago