Compute the following integrals:

$($a$){\displaystyle \underset{0}{\overset{1}{}}}\frac{6x^2+4}{x^3+2x+1}dx$

$($b$){\displaystyle \underset{0}{\overset{1}{}}}\frac{2x+1}{\sqrt[\phantom{2}]{x^2+x+2}}dx$

$($c$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}cos(x)sin(x)dx$

$($d$){\displaystyle \underset{0}{\overset{2}{}}}8x\sqrt[\phantom{2}]{5+x^2}dx$