$[15$ pts$]$ Evaluate the following integrals

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{t}^8\sqrt[\phantom{2}]{5+t^3}dt$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-sin(x)+cos(x)}{\sqrt[\phantom{2}]{cos(x)+sin(x)}}{2}^{\sqrt[\phantom{2}]{cos(x)+sin(x)}}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{4u-6}{u^2+6u+18}du$