$\int\frac{5x+7}{\left(x+2\right)^2}dx$

$\lim_{x\to\infty}\left(\frac{ln\left(x+1\right)-ln\left(x^2+2x+2\right)}{2\sqrt{x+1}}\right)$

$18+9+9x-3$

$-\frac{1}{2}\cdot\left(-3x+9\right)$

$\int\left(tan3x+cot3x\right)^2dx$

$\lim_{x\to0}\left(\frac{1}{x}-e^{-3x}\right)$

$x+\frac{\left(2x-3\right)}{9}+\frac{\left(x-1\right)}{3}=\frac{\left(12x+4\right)}{9}$