# Homework Help: Integration by partst

1. Feb 27, 2010

### Bryon

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

The the problem is integrate ln(sqrt(x^2-4)

2. Relevant equations

For this one u-sub does not work, which leads me to think that integration by parts is the way to go but am not sure how to finish it.

3. The attempt at a solution

u =1/2ln(x^2-4)
du = (1/2)(2x/(x^2-4)) = x^2/(x^2-4)

dv = dx ----> int dx = x = v

x(1/2ln(x^2-4)) - int (x^2)/(X^2-4)

I dont know what to do about the part in bold. Im thinking integration by part again but that doesnt look like it will work, unless there is one more integration to do. Any idea what i can try?

Thanks!

2. Feb 27, 2010

### holezch

I think parts can work again, since 1 / x^2 - 4 is easy enough to integrate, then you'll need to integrate xarctan(x/2) which should be fine

3. Feb 27, 2010

### Dick

Use polynomial division to write x^2/(x^2-4)=1+4/(x^2-4). Looks more to me like 'partial fractions' than 'parts'.

4. Feb 27, 2010

### Gavins

Write it as
ln(x^2 - 4)^1/2

and also note that it's a difference of 2 squares. Then just use the log properties to reduce this to something easier and you can then use integration by parts.

5. Feb 27, 2010

### Bryon

Thanks Dave! I did not see that, but it certainlly makes sense now.

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