How to integrate?

0π2xln(cosx)tanx dx\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
4 years, 4 months ago

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1 vote

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@Krishna Sharma @Ishan Dasgupta Samarendra @Pi Han Goh

Tanishq Varshney - 4 years, 4 months ago

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

Ishan Dasgupta Samarendra - 4 years, 4 months ago

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

Pi Han Goh - 4 years, 4 months ago

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First look remind me of β(a,b)4\frac{\beta'(a,b)}{4} at a=1/4,b=3/2a = -1/4, b = -3/2. But then there's that xx 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 - 4 years, 4 months ago

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

Ishan Dasgupta Samarendra - 4 years, 4 months ago

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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 - 4 years, 4 months ago

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Ok guys it was inspired from this

Tanishq Varshney - 4 years, 4 months ago

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

Ronak Agarwal - 4 years, 4 months ago

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

Kartik Sharma - 4 years, 4 months ago

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Check this link

Ronak Agarwal - 4 years, 4 months ago

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

Tanishq Varshney - 4 years, 4 months ago

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where.

Ronak Agarwal - 4 years, 4 months ago

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

Tanishq Varshney - 4 years, 4 months ago

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