# 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

Note by Tanishq Varshney
6 years, 1 month ago

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Sort by:

- 6 years, 1 month ago

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

- 6 years, 1 month ago

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

- 6 years, 1 month 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.

- 6 years, 1 month ago

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

- 6 years, 1 month ago

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

- 6 years, 1 month ago

Ok guys it was inspired from this

- 6 years, 1 month ago

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

- 6 years, 1 month ago

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

- 6 years, 1 month ago

- 6 years, 1 month ago

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

- 6 years, 1 month ago

where.

- 6 years, 1 month ago

Ok i'll mention u again there.

- 6 years, 1 month ago