int (sec(2x) + tan(2x)) dx Find the indefinite integral.

int(sec(2x)+tan(2x))dx=
Use additivity of integral: int (f(x)+g(x))dx=int f(x)dx+int g(x)dx. int sec(2x)dx+int tan(2x)dx=
Make the same substitution for both integrals: u=2x, du=2dx=>dx=(du)/2
1/2int sec u du+1/2int tan u du=
Now we have table integrals.
1/2ln|sec u+tan u|-1/2ln|cos u|+C
Return the substitution to obtain the final result.
1/2ln|sec(2x)+tan(2x)|-1/2ln|cos(2x)|+C 
http://integral-table.com/