Station $2$:

Evaluate each definite integral. $du=$

${\displaystyle \underset{\frac{22\sqrt[\phantom{2}]{3}}{3}}{\overset{2}{}}}\frac{1}{4x^2}dx$

${\displaystyle \underset{-6}{\overset{0}{}}}(x|3x6|)dx$

$\{\begin{array}{c}\text{:}[{\displaystyle \underset{\frac{2\sqrt[\phantom{2}]{3}}{3}}{\overset{\frac{2}{3}{x}^2}{}}}]\\ \frac{1}{4}\\ {\displaystyle \underset{\phantom{}}{\overset{2}{}}}& \frac{1}{x^2},& \frac{1}{4}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{1\frac{x^2}{4}}dx\\ {\displaystyle \underset{\frac{2}{4}}{\overset{\frac{21}{4}}{}}}& x^{-2}\\ \frac{1}{3}\end{array}dx$

${\displaystyle \underset{-1}{\overset{6}{}}}f(x)dx,f(x)=\{\begin{array}{ccc}2x& 1,& x0\\ 1,& x>0\end{array}$

Evaluate each indefinite integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cs{c}^{2}x}{cotx}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}-24xtan(4x^2-5)dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}9e^{3x}sin(e^{3x}-5)dx$