# 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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