$\frac{1+\sin2x}{\sin2x}$

$9x^2+42x=0$

$\int\left(e^{-y}\right)\cdot\left(y^3\right)dy$

$\int_0^{\frac{\pi}{3}}\left(\frac{\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}\right)dx$

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

$\left(3x^3-2x^2+x-5\right)+\left[\left(x^3+3x\right)-\left(x^2-x+2\right)+\left(-x^3+2x^2-3\right)\right]$

$\frac{x^4}{x^2-2}$