Solving an Integral Problem with Trig Substitution

[Temp0]

Homework Statement

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

Homework Equations

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.

 

[Dick]

Homework Statement

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

Homework Equations

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.

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

 

[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.

 

[Dick]

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.

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

 

[Temp0]

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