# Determine whether the expression is true or false: int tan(2x) xx dx = -1/2ln xx |\cos(2x)| + C

Determine whether the expression is true or false:
$\int \mathrm{tan}\left(2x\right)×dx=-\frac{1}{2}\mathrm{ln}×|\mathrm{cos}\left(2x\right)|+C$
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Luvottoq

$\int \mathrm{tan}\left(2x\right)×dx=-\frac{1}{2}\mathrm{ln}×|\mathrm{cos}\left(2x\right)|+C$

$I=\frac{1}{2}\int \mathrm{tan}\left(t\right)dt$
$I=\frac{1}{2}\mathrm{ln}|\mathrm{sec}\left(x\right)|+C,\mathrm{sec}\left(x\right)=\frac{1}{\mathrm{cos}\left(x\right)}={\left(\mathrm{cos}\left(x\right)\right)}^{-1},$
$I=-\frac{1}{2}\mathrm{ln}|\mathrm{cos}\left(x\right)|+C.$
Thus, the solution is true.