$\lim_{x\to1}ln\left(\frac{3x^3-1}{\cos\left(x-1\right)}\right)$

$8\tan^2-1=3tanx+4$

$\log\left(\frac{\left(1-cos\:x\right)}{\left(1+cos\:x\right)}\right)$

$\frac{1-3y^6+y^4-y^5}{y+y^4+3}$

$\int x\cos nydx$

$36x^2+7x-15$

$\lim_{x\to1}\left(\frac{\left|x-1\right|}{x^2-2x+1}\right)$