$1-\frac{1}{cot^2x}$

$\int\frac{6x+2}{\left(2x+1\right)\left(x^2+3\right)}dx$

$\cos\left(\pi-x\right)=-\cos x$

$\left(1+cot^2x\right)\left(1-cos2x\right)=2$

$\frac{n\left(2n+1\right)}{\left(n+1\right)\left(2n-1\right)}$

$8\left(k-4\right)$

$\int x\left(3x^3-12x\right)dx$