Evaluate the following integrals:

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(3x^2-2sin(x)+\frac{1}{x+1}+e^{2x})dx.$

$($b$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^2(x)cos(x)dx.$