Решете ∫ sin(x) wrt xsum_{tan(y)=1}^sqrt[cos(x)]{log(x)}y

$$\int{ \sin ( x ) }d x \sum_{ \tan ( y ) =1 }^{ \sqrt[ \cos ( x ) ]{ \log ( x ) } } y$$

Изчисляване

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

Диференциране по отношение на x

$$\frac{an\left(\log_{10}\left(x\right)\right)^{\frac{1}{\cos(x)}}\left(\frac{\left(\frac{y}{\cos(x)}\right)^{2}\left(2x\ln(x)\sin(x)\left(\cos(x)\right)^{2}-x\ln(x)\sin(2x)\ln(\ln(x))+\ln(\ln(10))x\ln(x)\sin(2x)-2\left(\cos(x)\right)^{2}\right)}{x\ln(x)}+2С\left(\sin(x)\ln(\ln(x))\times \left(\frac{y}{\cos(x)}\right)^{2}+\frac{y^{2}}{x\ln(x)\cos(x)}-\ln(\ln(10))\sin(x)\times \left(\frac{y}{\cos(x)}\right)^{2}\right)\right)}{2}$$