$\int\left(e^{\frac{1}{2}t}\left(\frac{3}{2}t^2\right)\right)dt$

$\left(-4x^2+3\right)^3$

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

$\left(4a^2+5x\right)\left(by-2bc\right)$

$\sin^2\left(44\right)$

$\int\left(\frac{sec^2\left(x\right)}{tan^3\left(x\right)}\right)dx$

$\lim_{x\to\infty}\frac{sin\:5x}{sin\:2x}$