$$a^4+4a^2-16$$

$$x^2+8x+53$$

$$\:\:\frac{\left(\sqrt{3y}-1\right)\left(\sqrt{3y}+1\right)}{5\left(3y^2-1\right)}$$

$$\int\left(x^2+x\right)^7\left(2x+1\right)dx$$

$$-x^2+7x$$

$$\frac{dy}{dx}=y\cdot sin\left(3x\right)+2\cdot sin\left(3x\right)+4\cdot y+8$$

$$\int\frac{x^3-x^2-3x+5}{x+5}dx$$