# A difficult integral

1. Sep 3, 2007

### Chen

How would one go about solving this?

$$\int_{ - \infty }^\infty {{1 \over {q^2 + C/\left| q \right|}}dq}$$

Or,

$$\int_0^\infty {{1 \over {q^2 + C/q}}dq}$$

With $$C > 0$$ obviously.

I came across this in a physics problem. A solution exists (verified by Mathematica).

Thanks,
Chen

2. Sep 3, 2007

### HallsofIvy

Staff Emeritus
Multiply both numerator and denominator by q:

$$\int_0^\infty {{q \over {q^3 + C}}dq}$$
q3+ C can be factored as (q+ C1/3)(q^2- C1/3q+ C2/3) and then use partial fractions. The exact form will depend upon whether q^2- c1/3q+ C can be factored with real numbers and that will depend upon C.

3. Sep 3, 2007

### Chen

Cheers. I should've thought of that myself. :-)

Chen