Question Number 213934 by ajfour last updated on 21/Nov/24
$$\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} \int_{\mathrm{0}} ^{\:{R}} \frac{\left({d}\theta\right)\left({dr}\right)\left({a}+{r}\mathrm{cos}\:\theta\right)}{\left({r}^{\mathrm{2}} +{x}^{\mathrm{2}} +\mathrm{2}{rx}\mathrm{cos}\:\theta\right)^{\mathrm{3}/\mathrm{2}} }\:={f}\left({a},{R}\right) \\ $$$${Find}\:{f}\left({a},\:{R}\right). \\ $$