$\lim_{x\to\infty}\left(\frac{sin\left(x\right)}{2tan\left(x\right)}.\left(1+tan\left(2x\right)^{\frac{1}{4}}\right)\right)$

$\int\left(-2x^{4n}\right)dx$

$\int\left(\frac{x^7}{\sqrt{x^8+11}}\right)dx$

$\frac{1}{3}\int\frac{1}{\frac{-17}{3}+\left(x-2\right)^2}dx$

$\frac{n}{n+3}+\frac{12n}{n-3}-\frac{9}{n^2-9}$

$1000^5$

$\frac{dy}{dx}=\frac{5x+xy^2}{2y+2}$