Solve ∫ sin(x) wrt xsum_{y=1}^sqrt[cosh(x)]{log(x)}yprod_y=1^cot(x)x

$$\int{ \sin ( x ) }d x \sum_{ y=1 }^{ \sqrt[ \cosh ( x ) ]{ \log ( x ) } } y \prod_{ y=1 }^{ \cot ( x ) } x$$

Evaluate

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

Differentiate w.r.t. x

$$\frac{\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}\left(\frac{x^{\cot(x)-1}\left(-\ln(x)\sin(x)\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}\left(\cosh(x)\cos(x)\right)^{2}+x\cos(x)\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}\left(\cosh(x)\ln(x)\right)^{2}+x\ln(x)\left(\cosh(x)\right)^{2}\left(\sin(x)\right)^{3}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}+2x\sinh(x)\ln(x)\cos(x)\ln(\ln(x))\left(\sin(x)\right)^{2}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}-2\ln(\ln(10))x\sinh(x)\ln(x)\cos(x)\left(\sin(x)\right)^{2}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}-\ln(x)\sin(x)\left(\cosh(x)\cos(x)\right)^{2}+x\cos(x)\left(\cosh(x)\ln(x)\right)^{2}-2\cosh(x)\cos(x)\left(\sin(x)\right)^{2}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}+x\sinh(x)\ln(x)\cos(x)\ln(\ln(x))\left(\sin(x)\right)^{2}+x\ln(x)\left(\cosh(x)\right)^{2}\left(\sin(x)\right)^{3}-\ln(\ln(10))x\sinh(x)\ln(x)\cos(x)\left(\sin(x)\right)^{2}-\cosh(x)\cos(x)\left(\sin(x)\right)^{2}\right)}{\ln(x)\left(\cosh(x)\sin(x)\right)^{2}}+С\left(-\frac{2\sinh(x)\ln(\ln(x))x^{\cot(x)}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}}{\left(\cosh(x)\right)^{2}}-\frac{\ln(x)x^{\cot(x)}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}}{\left(\sin(x)\right)^{2}}+\frac{2x^{\cot(x)-1}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}}{\cosh(x)\ln(x)}+\frac{2\ln(\ln(10))\sinh(x)x^{\cot(x)}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}}{\left(\cosh(x)\right)^{2}}+\cot(x)x^{\cot(x)-1}\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cosh(x)}}-\frac{\sinh(x)\ln(\ln(x))x^{\cot(x)}}{\left(\cosh(x)\right)^{2}}-\frac{\ln(x)x^{\cot(x)}}{\left(\sin(x)\right)^{2}}+\frac{\ln(\ln(10))\sinh(x)x^{\cot(x)}}{\left(\cosh(x)\right)^{2}}+\frac{x^{\cot(x)-1}}{\cosh(x)\ln(x)}+\cot(x)x^{\cot(x)-1}\right)\right)}{2}$$