Integral 1

Calculus Level 5

Evaluate:

\[\large \int_{0}^{\pi/2} \sin x \cos x \sqrt{\tan x}\ln (\tan x) \, dx\]

The answer can be expressed as \(\dfrac{\pi\left(b-\pi\right)\sqrt c}a\), where \(a\), \(b\), and \(c\) are positive integers and \(c\) is square-free; find \(100a+10b+c\).

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