a$)$ Evaluate the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(lnx+\frac{cosx}{2\sqrt[\phantom{2}]{3+sinx}})dx(10$ points$)$

Solution:

b$)$ Find $f(x)$ in the formula below? $(10$ points$)$

Solution:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(x)dx=\frac{3}{2}lnx-\frac{1}{2}ln(x+2)+C$