How to integrate?

$\large{\displaystyle \int^{\frac{\pi}{2}}_{0} x \ln(\cos x) \sqrt{\tan x} \text{ d}x}$

plz post ur method and i dont know its answer

#Calculus

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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`	$\sum_{i=1}^3$
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Comments

@Krishna Sharma @Ishan Dasgupta Samarendra @Pi Han Goh

Tanishq Varshney - 6 years ago

I'll try it though I don't know if I can get an answer.

User 123 - 6 years ago

Are you sure it has a closed form? If yes, what makes you say that?

Pi Han Goh - 6 years ago

First look remind me of $\frac{\beta'(a,b)}{4}$ at $a = -1/4, b = -3/2$ . But then there's that $x$ which reminds me of this and I think it is essentially the same problem. But since I've not solved that problem, I can only help you until here. There maybe solvers of that problem out there and they can surely help.

Kartik Sharma - 6 years ago

@Tanishq Varshney This seems to involve Complex Contour Integration. Unfortunately I don't know Contour Integration. @Kartik Sharma Please could you help?

User 123 - 6 years ago

I don't think it involves contour integration. It might be involving but then it is not that smooth to notice that easily.

Kartik Sharma - 6 years ago

Ok guys it was inspired from this

Tanishq Varshney - 6 years ago

Closed form has been posted on math-stack exchange, I will post the link soon.

Ronak Agarwal - 6 years ago

I think that link will give a hint of how to do your problem.

Kartik Sharma - 6 years ago

Check this link

Ronak Agarwal - 6 years ago

Thanx for the link , can u plz reply to the post where i commented on one of ur solution

Tanishq Varshney - 6 years ago

where.

Ronak Agarwal - 6 years ago

@Ronak Agarwal – Ok i'll mention u again there.

Tanishq Varshney - 6 years 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}`	$\boxed{123}$