Question Number 21634 by Isse last updated on 29/Sep/17
$$\int\mathrm{3}{tan}\mathrm{2}{t} \\ $$
Answered by Joel577 last updated on 30/Sep/17
$${I}\:=\:\int\:\mathrm{3tan}\:\mathrm{2}{t}\:{dt} \\ $$$$\mathrm{Let}\:{u}\:=\:\mathrm{2}{t}\:\:\rightarrow\:\:{du}\:=\:\mathrm{2}\:{dt} \\ $$$${I}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\int\:\mathrm{tan}\:{u}\:{du} \\ $$$$\:\:\:\:=\:−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{cos}\:{u}\mid\:+\:{C} \\ $$$$\:\:\:\:=\:−\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{2}{t}\mid\:+\:{C} \\ $$