Exercises $77-84,$ evaluate the definite integral. graphing utility to verify your result.

$77.{\displaystyle \underset{-2}{\overset{1}{}}}x(x^2-6)dx$

$79.{\displaystyle \underset{0}{\overset{3}{}}}\frac{1}{\sqrt[\phantom{2}]{1+x}}dx$

$81.2{\displaystyle \underset{0}{\overset{1}{}}}(y+1)\sqrt[\phantom{2}]{1-y}dy$

$83.{\displaystyle \underset{0}{\overset{}{}}}cos(\frac{x}{2}dx)$