# How to integrate this?

1. Oct 23, 2014

### Math10

1. The problem statement, all variables and given/known data
How to integrate dz/(z^2+2z/x)?

2. Relevant equations
None.

3. The attempt at a solution
I did partial fractions but it doesn't seem to work.
A/z+B/(z+2/x)=1

2. Oct 23, 2014

### ShayanJ

Try completing the square!

3. Oct 24, 2014

### dslowik

The thing to do for partial fractions would be to solve:
1/(z^2+2z/x) = 1 / z(z+2/x) = A/z+B/(z+2/x)
for A and B, and then it can be integrated to logs.

Or, you can complete the square and you're left with an integral that yields a hyperbolic trig solution which can be expressed in terms of logs:
http://en.wikipedia.org/wiki/Hyperbolic_function

So you get log absolute values when integrating 1/z at negative z...,
and there are corresponding domain restrictions on the validity of the hyperbolic trig solution.
When you take care, you can arrive at the two methods yielding the same solution over their common domain of validity: z=(-2/x,0) (assuming x>0).

4. Oct 24, 2014

### vela

Staff Emeritus
That would be because the righthand side shouldn't be equal to 1.