When \(x\) meets trigonometry and logarithms...

Calculus Level 3

The integral of x sin (ln x) with respect to x can be expressed as \(\frac{\alpha}{\beta} \) \(x^2 \) sin (ln x) - \(\frac{\gamma}{\delta} \) \(x^2 \) cos (ln x) + c where c is an arbitrary constant. Suppose gcd (\(\alpha\), \(\beta\)) =1 and gcd (\(\gamma\), \(\delta\)) = 1, find \(\alpha\) + \(\beta\) + \(\gamma\) + \(\delta\) ?

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