Question Number 154422 by peter frank last updated on 18/Sep/21
$$\int\frac{\mathrm{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{a}^{\mathrm{4}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{4}} \mathrm{cos}\:^{\mathrm{2}} \theta}\mathrm{d}\theta \\ $$