Consider the integral tan(x)ln(3cos(x)) dx\displaystyle \int-{\tan{{\left({x}\right)}}}\cdot{\ln{{\left({3}{\cos{{\left({x}\right)}}}\right)}}}\ {d}{x}:

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

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}=  

b) After performing the substitution, you obtain the integral

\displaystyle \int  

c) Once we integrate and substitute, the final answer in terms of x is: