Question Number 206557 by luciferit last updated on 18/Apr/24
Answered by Frix last updated on 18/Apr/24
$$\mathrm{Without}\:\mathrm{substitution}: \\ $$$$\int\frac{\mathrm{3}+\mathrm{2sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}^{\mathrm{2}} \:{x}}{dx}=\int\left(\frac{\mathrm{5}}{\mathrm{cos}^{\mathrm{2}} \:{x}}−\mathrm{2}\right){dx}= \\ $$$$=\mathrm{5tan}\:{x}\:−\mathrm{2}{x}\:+{C} \\ $$