Solve ∫ sin ( x ) wrt x sum_{ y=1 }^ sqrt[ cosh ( x ) ]{ log ( x ) } y prod_ y=1 ^ cot ( x ) x limit (as x approaches 2) of left( ln ( x)right)

$$\int{ \sin ( x ) }d x \sum_{ y=1 }^{ \sqrt[ \cosh ( x ) ]{ \log ( x ) } } y \prod_{ y=1 }^{ \cot ( x ) } x \lim_{ x \rightarrow 2 } \left( \ln ( x ) \right)$$

Evaluate

$$\frac{\left(-\cos(x)+С\right)\log(x)^{\frac{1}{\cosh(x)}}\left(\ln(2)x\right)^{\cot(x)}\left(\log(x)^{\frac{1}{\cosh(x)}}+1\right)}{2}$$

Differentiate w.r.t. x

$$\frac{\sin(x)\left(\ln(2)x\right)^{\cot(x)}\left(\log(x)^{\frac{1}{\cosh(x)}}+\log(x)^{\frac{2}{\cosh(x)}}\right)}{2}$$