$\lim_{x\to0}\:\frac{1}{sinx}-\frac{1}{x^2}$

$\csc^2ydx=\csc xdy$

$-2+\left(-11+2-\left|-3-4+1\right|-8\right)-2$

$\frac{dy}{dx}=\frac{y\left(3x-1\right)}{x}$

$\int\frac{e^w}{\left(e^w\:-1\right)\left(e^w\:+\:4\right)}dw$

$2x^2\:+\:15x\:+\:27$

$\int_{0}^{2}z^{3}\sqrt{z^{2}+4}dz$