$\int\left(11x-10\right)^9\:dx$

$4^{2x+2}-2\left(4^{x+1}\right)+1=0$

$3\cos3x\cdot\cos5x-5\sin3x\cdot\sin5x$

$3t+7t^2-t$

$\left(\cos\left(x\right)\right)^2-\left(\sin\left(x\right)\right)^2=\frac{5}{4}$

$\frac{dy}{dt}=\frac{y+1}{t\left(y-1\right)}$

$\frac{x^3+2x+1}{x+1}$