$(50$ points$)$ Evaluate the following integrals.

$($a$){\displaystyle \underset{-1}{\overset{-\frac{1}{2}}{}}}\frac{1}{x^2}si{n}^2(1+\frac{1}{x})dx.$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos\sqrt[\phantom{2}]{x}dx.$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{\sqrt[\phantom{2}]{1-x^4}}dx.$