$\int_1^{\infty}u\cdot e^{-\frac{\left(u-1\right)}{12}}du$

$\cos\left(4x\right)-\sin\left(4x\right)=1-2\sin^2\left(x\right)$

$\cos\left(x\right)\sin\left(x+\frac{\pi}{2}\right)-sin\left(x\right)cos\left(\frac{\pi}{2}+x\right)=1$

$\frac{5w^{-2}}{w^{-7}}$

$\lim_{t\to infnity}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

$4\:-\:8\:-\:\left(-16\right)$

$-\frac{20a^9b^7}{5a^4b^6}$