$\int\cos^7ydy$

$\int\frac{\cos\left(t\right)}{\sin\left(t\right)+\sin^2\left(t\right)}dt$

$e^ty\frac{dy}{dt}=e^{-y}+e^{-2t-y}$

$\int e^{4x}-5\sin\left(x\right)dx$

$\lim inf\left(\left(1+2x\right)\frac{1}{2\ln\left(x\right)}\right)$

$\frac{1}{n^{2\:}}+\frac{1}{m^2}$

$\frac{2x+2}{x+2}-\frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x+4\right)}$