$\log\left(x\right)-\frac{1}{2}\log\left(x+1\right)-\log\:\left(x-1\right)$

$\int\frac{x^3+23}{x^2+7x+12}dx$

$\frac{2cos\left(2a\right)}{sin\left(2a\right)}=cot\left(a\right)-tan\left(a\right)$

$-40x^2+5x$

$\frac{dy}{dx}=x+5$

$\frac{d}{dz}y=6^{z^5}$

$\frac{d}{dx}-7$