$\lim_{x\to0}\frac{5^x-1}{\sin\left(2x\right)}$

$\lim_{n\to\infty}\:\frac{2^{n+2}+1}{1^n+1}$

$\left(y+6\right)\left(y-6\right)-\left(y+9\right)^2$

$\frac{5x}{3x^2+5x}$

$5x-9<\:2x+\:15$

$\frac{5x^3-2x-8}{x+1}$

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x+\frac{3\pi}{2}\right)sin\left(nx\right)dx$