Integrating Gullstrand-Plainleve Coordinates in Kerr Metric

[stevebd1]

I'm looking at Gullstrand-plainleve coordinates in Kerr metric. While on the whole, it seems pretty straight forward, I found the integral aspect a little inaccessible. I've had a look at various web pages regarding integrals but to be honest, I don't know where to start with the following. Any insight would be appreciated.

$$\delta=a^2sin(2\theta)\int_r^{+\infty} \frac{v\Omega}{\varpi^2}dr$$

where

$$\Omega=\frac{2Mar}{\rho^2(r^2+a^2)+2Ma^2rsin^2\theta}$$

$$\varpi^2=r^2+a^2+\frac{2Mra^2}{\rho^2}sin^2\theta$$

$$v=\frac{\sqrt{2Mr(r^2+a^2)}}{\rho^2}$$

$$\rho^2=r^2+a^2cos^2\theta$$

 

[stevebd1]

I used an online integral calculator (replacing r with x) which produced the following results-

http://www.majhost.com/gallery/stevebd/science/msp22530435753657184888_189.gif

Does this look right? (unfortunately it didn't have the means to incorporate the limits of r and +∞. What impact would that have on the results?).

online integral calculator-
http://integrals.wolfram.com/index.jsp