Question $1$ evlauate the four integrals below by hand.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{2x}cos4xdx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}co{s}^{6}xdx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{\sqrt[\phantom{2}]{x^2-4}}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2+3x-1}{x^3+x^2-2x}dx$