Question Number 196276 by SaRahAli last updated on 21/Aug/23
Answered by MM42 last updated on 21/Aug/23
$$\int\:\frac{{dx}}{\mathrm{1}+{sin}\mathrm{2}{x}}\:=\int\:\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}+{tanx}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\overset{\mathrm{1}+{tanx}={u}} {=}\:\int\:\frac{{du}}{{u}}\:={lnu}+{c} \\ $$$$={ln}\left(\mathrm{1}+{tanx}\right)+{c}\:\checkmark \\ $$$$ \\ $$