Use $u$ substitution to complete the following computation. All values should be exact. For example, values like $\sqrt[\phantom{2}]{2}$ should not be approximated with a decimal.

Consider the definite integral ${\displaystyle \underset{\frac{1}{2}*}{\overset{2*}{}}}-sin(x)e^{2cos(x)}dx.$

a$)$ This can be transformed into a basic integral by letting

$u=$ and

$du=$

b$)$ Performing the substitution yields the integral

c$)$ Integrating with respect to $u$ yields the antiderivative $G(u)=C$

d$)$ After evaluating, the final answer is ${\displaystyle \underset{\frac{1}{2}*}{\overset{2*}{}}}-sin(x)e^{2cos(x)}dx=$