$\left(-12\right):4x\left(-5\right)-20:\left(-2\right)$

$\frac{5csc\left(x\right)}{csc\left(x\right)-cot\left(x\right)}=5csc\left(x\right)\left(csc\left(x\right)+cot\left(x\right)\right)$

$\frac{x^2+5x+7}{x+3}$

$-3\left(a-b\right)-7\left(2a+b\right)$

$\int8te^{7t}\:dt$

$\int\frac{\left(\sqrt{x}\right)}{2x^2+2x}dx$

$\lim_{x\to1}\left(\arctan\left(x\right)\right)^{\frac{1}{2x}}$