$\lim_{x\to0}\left(\cot\left(8x\right)-\frac{1}{8x}\right)$

$\int\frac{\left(x^3-x\right)}{\sqrt{x}}dx$

$2^{3t+2}=2^{t-8}$

$\frac{x^4+2x^2+1}{x+1}$

$1\left(x\right)^2\cdot\cos\left(x\right)^2$

$\frac{\csc^2\left(t\right)}{\sec\left(t\right)}=\csc\left(t\right)\tan\left(t\right)$

$\int\frac{7}{\sqrt{x}\:e^{-\sqrt{x}}}\:dx$