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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
\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
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