$\int-6x\:dx$

$\frac{5}{x-5}=\frac{x}{x-5}-1$

$-3^4-3\left(-3\right)^3+5\left(-3\right)^2-9\left(-3\right)+6$

$\int2x^3cos\:\left(x^2\right)dx$

$\lim_{x\to0}\left(\frac{\left(5^x\:-\:1\right)\left(4^x\:-\:1\right)}{\left(3^x\:-\:1\right)\left(6^x\:-\:1\right)}\right)$

$\frac{dy}{dx}-x^2y=y+x^2$

$\left(x^2-2\right)\left(x^2+2x+4\right)$