Question $6.$ Find the general solution to:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}tan(t)dt=-ln|cos(t)|+C,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sec(t)dt=ln|sec(t)+tan(t)|+C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cot(t)dt=ln|sin(t)|+C,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}csc(t)dt=-ln|csc(t)+cot(t)|+C{y}^{\text{'}\text{'}}+4y=8tan(2t),\frac{-}{4}$

Hint: Here are some integrals you might find useful

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}tan(t)dt=-ln|cos(t)|+C,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sec(t)dt=ln|sec(t)+tan(t)|+C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cot(t)dt=ln|sin(t)|+C,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}csc(t)dt=-ln|csc(t)+cot(t)|+C$