Evaluate the following integral.

${\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}\frac{co{s}^{4}x}{\sqrt[\phantom{2}]{1-sinx}}dx$

${\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}\frac{co{s}^{4}x}{\sqrt[\phantom{2}]{1-sinx}}dx=$

$($Type an exact answer.$)$