# Math Help - Integration

1. ## Integration

Stuck on trying to integrate

(4 + 3sec(2x))^2

2. If we expand it out, we get:

$\int\left[16+24sec(2x)+9sec^{2}(2x)\right]dx$

Now, integrate term by term and it ain't bad.

3. Originally Posted by galactus
If we expand it out, we get:

$\int\left[16+24sec(2x)+9sec^{2}(2x)\right]dx$

Now, integrate term by term and it ain't bad.
Problem is I don't know the integral of 24sec(2x) I know sec^2(x) becomes tan(x). Thats where I was getting stuck, I put the full equation out so that I could check if I had expanded correctly.

4. Originally Posted by Beard
Problem is I don't know the integral of 24sec(2x) I know sec^2(x) becomes tan(x). Thats where I was getting stuck, I put the full equation out so that I could check if I had expanded correctly.
The integral of the secant of x is a tricky one that is hard to see if you don't know it. Consider $\sec(x) * \frac{\sec(x)+\tan(x)}{\sec(x)+\tan(x)}$ and make a u-substitution. Hint:the answer contains a natural log.