# Complicated Definite Double Integral

by dBrandon/dC
Tags: complicated, definite, double, integral
 PF Gold P: 864 The "r" part of the integral is doable. I get $$P=\int_{0}^{\pi}2\rho Gmdr^{2}a\sin{a}\dot ( \ln{\sqrt{r^{2}+d^{2}-\cos{a}} +r} -\frac{r}{\sqrt{r^{2}+d^{2}-\cos{a}}})da\left|^{r=6.275*10^6}_{r=6.175*10^6}$$ Integrating the "a" part seems like it should be a nightmare, though. You could do a substitution u=-cos(a) if it wasn't for that a sitting outside. It's probably not expressible in elementary functions. Could you just evaluate it numerically?
 Engineering Sci Advisor HW Helper Thanks P: 6,959 Starting with the a integral, $$\int \frac{a \sin a\, da}{(b^2 - \cos a)^{3/2}}$$ is an elliptic function of the 3rd kind according to http://integrals.wolfram.com. My knowledge of elliptic functions doesn't extend to knowing if your definite integral equals something nice, but at least that's a start.