Another Integral Problem

1. Feb 9, 2014

Temp0

1. The problem statement, all variables and given/known data

http://i.imgur.com/u1De0i3.png

2. Relevant equations

3. The attempt at a solution

So I notice that the bottom is in the form x^2 - a^2 where a = 7, so I use trig substitution to start this off.

x = 7secθ, dx = 7secθtanθ, and finally, x^2 - 49 = 49sec(θ)^2 - 49 = 49 tan^2(θ)
Substituting into the integral, I get
7∫(sec^2(θ) - secθ) dθ, which basically turns into:
7tanθ - 7 ln |secθ + tanθ|.
After putting x back into the equation, I end up with:
√(x^2-49) - 7 ln|(x/7) + (√(x^2-49)/7)| + C
I would just like your help in checking my answers, because I don't get any of the answers provided in the multiple choice, and i'm always hesitant to pick "none of the above". Thank you.

2. Feb 9, 2014

Dick

One of those answers differs from your answer by a constant.

3. Feb 9, 2014

Temp0

What do you mean? Hmm, I can't really see any way to rearrange it like that, I think I know the one you're talking about though.

4. Feb 9, 2014

Dick

For example, log(x/7)=log(x)-log(7).

5. Feb 9, 2014

Temp0

Ohhhh! Let's see if I can go any further now, thanks alot.