Monstrous Integral

Level pending

As usually I'll post a problem found in a book I'm currently working with. The book is named "Romanian Mathematical Olympiads 1954-2003" and the problem is from 1975 or 1976 Olympiad for Technical Colleges.

If \(I=\displaystyle\int^1_0 \dfrac{x^2e^{\arctan x}}{\sqrt{x^2+1}}\), find the value of \(4I\).

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