Integrate.

1. $\int 2 \operatorname { sec } ( x ) \operatorname { tan } ( x ) d x$  

   First Step (a):

   $=2\int \text{sec}(x)\text{tan}(x)dx$

   It might be easier to integrate if you factor out the coefficient first.

2. $\int \operatorname { csc } ^ { 2 } ( 2 x ) d x$  

   Answer (b):

   $=-\frac{1}{a}\text{cot}(2x)+C$

   What is the value of $a$?