Integrable?

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

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Pi Han Goh @Kartik Sharma @Ishan Singh

Tanishq Varshney - 5 years, 6 months ago

What makes you think it has a closed form?

Pi Han Goh - 5 years, 6 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.

Tanishq Varshney - 5 years, 6 months ago

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

Pi Han Goh - 5 years, 6 months ago

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

Tanishq Varshney - 5 years, 6 months ago

@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 - 5 years, 6 months ago

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

Pi Han Goh - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$