The next step $in$ evaluating the integral will $beto$ use the trig identity $to$ rewrite

the integrand $in$ terms $of$ only secant $or$ cosecant. Once you have done that, you

can break the integral into a difference $of$ two separate integrals. Write

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}co{t}^{2}xcs{c}^{7}xdxas$ a difference $of$ integrals $of$ odd powers $of$ secant $orcosecent.$

Start with the highest power.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx-{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx$

Now, there are many more steps $togo,$ but $we$ will stop there! This $is$ a good

start!