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

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

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TopNewest@Pi Han Goh @Kartik Sharma @Ishan Singh – Tanishq Varshney · 10 months, 2 weeks ago

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– Pi Han Goh · 10 months, 2 weeks ago

What makes you think it has a closed form?Log in to reply

– Tanishq Varshney · 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.Log in to reply

– Pi Han Goh · 10 months, 2 weeks ago

You didn't answer my question: is there a closed form?Log in to reply

– Tanishq Varshney · 10 months, 2 weeks ago

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

– Pi Han Goh · 10 months, 2 weeks ago

Can you at least tell where/how you form this integral?Log in to reply

– Pi Han Goh · 10 months, 2 weeks ago

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