Question Number 34284 by math khazana by abdo last updated on 03/May/18
$${find}\:\:\int\:\:\:\frac{{dt}}{{sin}\left(\mathrm{2}{t}\right)} \\ $$
Commented by math khazana by abdo last updated on 07/May/18
$${changement}\:{tant}=\:{x}\:{give} \\ $$$$\int\:\:\:\:\:\frac{{dt}}{{sin}\left(\mathrm{2}{t}\right)}\:\:=\:\int\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }}\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\:\frac{{dx}}{{x}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}{ln}\mid{x}\mid\:+{c}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{ln}\mid{tant}\mid\:+{c}\:. \\ $$