$\frac{dy}{dx}ln\left(tan\left(ln\left(\frac{x}{y}\right)\right)\right)$

$\int\left(x-x^7\right)^4dx$

$\int\left(2x-2y\right)dy$

$2x^8+x^{16}+1$

$\int cost^2\:2tdt$

$\int_{-\frac{\pi}{3}}^{\frac{\pi}{3}}\left(\sin\left(x\right)-\cos\left(x\right)\right)^2dx$

$\:\int\frac{-\csc^2\left(x\right)}{\cot^3\left(x\right)}dx$