помогите решить интеграл dx/(5+3*sinx)

t=tg(x/2)
sin(x) = 2t/(1+t^2)
dx = 2dt/(1+t^2)

2 / ((1+t^2)*(5+3*2t/(1+t^2))) dt = 2/(5t^2 +6t +5) dt =2/5 dt/(t^2 +6/5t +1) = 2/5 dt/ ( (t+3/5)^2 +16/25) )
интегрируем
2/5 *5/4 * arctg( 5/4 (t+3/5) )+C = 1/2 * arctg(5/4 tg(x/2) +3/4)+C
Ответ : integral dx/(5+3sin(x)) = 1/2 * arctg(5/4 tg(x/2) +3/4)+C