$\int\left(e^{at}\sin\left(bt\right)\right)dt$

$\lim_{x\to9}\left(\frac{3-\sqrt{x}}{81-x^2}\right)$

$\lim_{x\to\infty}\left(\frac{5^x-9x-7}{2^x-x-2}\right)$

$-21-\left(-112\right)-79$

$-y^3dy=xdx$

$\int\left(x^{-1}\left(2x^4-5x+3\sqrt{x}-7\right)\right)dx$

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