$\int\left(\frac{1}{\sqrt{x}}e^{\sqrt{x}}\right)dx$

$\int\:\frac{3t^2+t+4}{t^3+t}dt$

$\lim_{x\to0}\left(\frac{\sin\left(3y\right)\cot\left(4y\right)}{y\cot\left(5y\right)}\right)$

$784-32\left(13\right)$

$y=\frac{e^{x^2-3x}\sqrt[5]{x}}{\left(x+1\right)^4}$

$\int\frac{1}{x^3-2x^2-4x+8}dx$

$\int x\cos\left(x^2+4\right)\sin\left(x^2+4\right)dx$