Помогите ,пожалуйста, решить неопределенный интеграл. dx/(5-4sinx)

Int( dx/ (5 - 4 * sin (x) ) ) = Int( dx/ (1 + 4 * ( 1 - 2 * sin (x/2) * cos(x/2) ) ) =
Int( dx/ ( cos(x/2)^2 + sin(x/2)^2 + 4 * ( cos(x/2)^2 + sin(x/2)^2 - 2 * sin (x/2) * cos(x/2) ) ) ) = Int ( d (1/ cos(x/2) ^2) / (1 + tg(x/2)^2 + 4 * (1 + tg(x/2)^2 - 2 * tg(x/2) ) ) ) = | tg(x/2) = t | = 2* Int (dt / (1+ t^2 + 4 + 4*t^2 - 8*t) ) = 2* Int (dt / (5*t^2 - 8*t +5)) = 2 * Int (dt / (5* (t - 0.8)^2 + 5*(1 - 0.64) )) = 2/(5 * 0.6) * Int (d( (t - 0.8)/0.6) /(1 + ((t - 0.8)/0.6) ^2) = 2/3 * arctg ( (t - 0.8)/0.6) + C = 2/3 * arctg (5/3 * tg(x/2) - 4/3) + C