When $x$ meets trigonometry and logarithms...

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 $\alpha$ + $\beta$ + $\gamma$ + $\delta$ ?