int(0)^(pi/2) sin 2x tan^(-1) (sin x) dx...

`int_(0)^(pi/2) sin 2x tan^(-1) (sin x) dx`

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To solve the integral \[ I = \int_{0}^{\frac{\pi}{2}} \sin(2x) \tan^{-1}(\sin x) \, dx, \] we will follow a systematic approach. ...

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