Solving a Difficult Integral - Physics Problem by Chen

[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

 

[HallsofIvy]

Multiply both numerator and denominator by q:


$$\int_0^\infty {{q \over {q^3 + C}}dq}$$
q³+ C can be factored as (q+ C^1/3)(q^2- C^1/3q+ C^2/3) and then use partial fractions. The exact form will depend upon whether q^2- c^1/3q+ C can be factored with real numbers and that will depend upon C.

 

[Chen]

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

Chen