# Another Integral Problem

## Homework Statement

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

## 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 Helper

## Homework Statement

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

## 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.

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