Evaluate the integral

a$.{\displaystyle \underset{0}{\overset{1}{}}}(\frac{4}{1t^2}(hat())\frac{2t}{1t^2}(hat(k)))dt$

b$.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}(3si{n}^{2}tcost(hat())3sintco{s}^{2}t(hat())2sintcost(hat(k)))dt$

c$.{\displaystyle \underset{1}{\overset{2}{}}}(t^2(hat())t\sqrt[\phantom{2}]{t-1}(hat())tsint(hat(k)))dt$