$\lim_{\theta\to\frac{\pi}{4}\frac{\cos\left(2\theta\right)}{\sqrt{2}\cos\left(\theta\right)-1}}$

$\frac{dy}{dx}=x\:-\:2xy$

$\int_1^0\left(x-1\right)^3-\left(x-1\right)dx$

$\left(xy^2+20\right)\left(xy^2-4\right)$

$\int\frac{\left(4x+3\right)}{e^x}dx$

$-30\cdot40$

$\frac{a^{11}+1}{a-1}$