"I am Back" says Integration Part 9

Calculus Level 5

\[ \large \int_0^\infty \dfrac{\sin x}{x^2} (1-e^{-x} ) \, dx \]

If the above integral above can be expressed as

\[ \dfrac \pi A + \ln (\sqrt B ), \]

where \(A\) and \(B\) are integers, find \(A+B\).

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