Integral $$$ g(a)= \int_{0}^{\frac{\pi}{2}} \frac{\arctan(a \tan x)}{\tan x}dx $$$

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edited Dec 16, 2019 at 17:07

Integral $$ g(a)= \int_{0}^{\frac{\pi}{2}} \frac{\arctan(a \tan x)}{\tan x}dx $$

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edited Dec 16, 2019 at 17:07

I am having trouble calculating this integral:

$$ g(a) \int_{0}^{\frac{\pi}{2}} \frac{\arctan(a \tan x)}{\tan x}dx $$$$ g(a) = \int_{0}^{\frac{\pi}{2}} \frac{\arctan(a \tan x)}{\tan x}dx $$

I tried calculating $g'(a)$ but then I get stuck.

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asked Dec 16, 2019 at 17:03

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