Evaluate $\int_{0}^{1} \frac{\log(x)}{\sqrt{1 - x^2}}$ complex integration

Asked Dec 25 '14 at 22:15

Active Apr 03 '19 at 01:23

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Evaluate: $$2\cdot\int_{0}^{1} \frac{\log(x)}{\sqrt{1 - x^2}} dx$$

Using Complex Integration.

I want to do something with the unit circle, but I am not quite sure how to work-around with the unit circle and the integral.

Will someone have an idea?

Thanks =)

edited Apr 03 '19 at 01:23

asked Dec 25 '14 at 22:15

Amad27

The answer is already here http://math.stackexchange.com/a/119877/131872 (similar integral). – user2345215 Dec 25 '14 at 22:37
You have already asked the same question in disguise, with $$\int_{0}^{\pi/2}\log\sin t,dt.$$ – Jack D'Aurizio Dec 25 '14 at 23:26

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