$\lim_{x\to\infty}\:\frac{x+2\sqrt{x+1}}{x+\sqrt{x}}$

$\frac{\left(1+\sin x\right)\left(1-\sin x\right)}{\cot^2\left(x\right)}$

$\int\frac{5x^2+36x+48}{x\left(x-1\right)^2}dx$

$\frac{2x^{-2}y^{-2}}{4y^{-5}}$

$\int15x^4dx$

$\int_{-5}^1\left(-2x^2-4x-3\right)dx$

$\frac{a^2-2a-3}{a+4}$