$6\sin\left(2x\right)\cos\left(2x\right)$

$\frac{d}{dx}x-\cos2x$

$\frac{sin^2}{\frac{sin}{cos}}$

$2\left(2^{k+1}\:-1\right)=2\left(2^k-1\right)+2^{k+1}$

$\log3\left(x^2-2x\right)-\log3\left(x-2\right)=2$

$\int x^2\sin\left(x\right)\cos\left(x\right)dx$

$\int\left(2w^3\ln\left(3w\right)\right)dw$