$\lim_{x\to\infty}\left(\frac{\left(-2x-1\right)\left(x+3\right)^2}{\left(x+4\right)^2\left(x-7\right)}\right)$

$\int\frac{x^3+3x^2}{x^2+1}dx$

$\int_0^{\infty}\sin\left(2x\right)dx$

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

$\frac{d}{dx}\sin^{-1}1-w$

$\int e^{-3x}sin6xdx$

$\int\frac{\sqrt{16-x^2}}{2}dx$