Подскажите, пожалуйста, как решить int dx/sin 2x ?

int dx/sin 2x = int dx/(2 * sin x * cos x) = 1/2 * int dx/(sin x * cos x) =
= 1/2 * int cos x dx/(sin x * cos^2 x) = 1/2 * int cos x/sin x d(tg x) =
= 1/2 * int 1/tg x d(tg x) = | t = tg x | = 1/2 * int 1/t dt =
= 1/2 * ln |t| + C = | t = tg x | = 1/2 * ln |tg x| + C